Question 1: Palette 1/454

Advance 2046 MCQ

A chain consisting of 5 links each of mass $0.1\mathrm{kg}$ is lifted vertically with a constant acceleration of $2.5\mathrm{ms}^{-2}$ . The force of interaction between the top link and the link immediately below it, will be

A

$6.15\mathrm{N}$

B

$4.92\mathrm{N}$

C

$3.69\mathrm{N}$

D

$2046\mathrm{N}$

Question 2: Palette 2/454

Advance Online April 2019 MCQ

If $10^{22}$ gas molecules each of mass $10^{-26}$ kg collide with a surface (perpendicular to it) elastically per second over an area $1\mathrm{m}^2$ with a speed $10^{4}\mathrm{ms}^{-1}$ , the pressure exerted by the gas molecules will be of the order of

A

$1\mathrm{Nm}^{-2}$

B

$2\mathrm{Nm}^{-2}$

C

$3\mathrm{Nm}^{-2}$

D

$4\mathrm{Nm}^{-2}$

Question 3: Palette 3/454

Advance Online April 2019 MCQ

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum height $(p-h)$ diagram is

A

B

C

D

Question 4: Palette 4/454

Advance Online April 2019 MCQ

A ball is thrown upward with an initial velocity $V_{0}$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma v^{2}$ (where m is mass of the ball, v is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is

A

$\frac{1}{\sqrt{\gamma g}}\sin^{-1}\left(\sqrt{\frac{\gamma}{g}} V_0\right)$

B

$\frac{1}{\sqrt{\gamma g}}\ln \left(1 + \sqrt{\frac{\gamma}{g}} V_0\right)$

C

$\frac{1}{\sqrt{\gamma g}}\tan^{-1}\left(\sqrt{\frac{\gamma}{g}}V_{0}\right)$

D

$\frac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\frac{2\gamma}{g}} V_0\right)$

Question 5: Palette 5/454

Advance Online April 2019 MCQ

Two blocks A and B of masses $m_{A}=1$ kg and $m_{B}=3$ kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is [Take $g=10\ ms^{-2}$ ]

A

40 N

B

12N

C

16 N

D

8 N

Question 6: Palette 6/454

Advance Online April 2019 MCQ

[Online April 2019] A block of mass 5 is kg (i) pushed in case (A) and (ii) pulled in case (B), by a force $F = 20 \, \text{N}$ , making an angle of $30^\circ$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$ . The difference between the accelerations of the block, in case (B) and case (A) will be $(g = 10 \, \text{ms}^{-2})$

A

C

$0 \, ms^{-2}$

D

$0.8 \, ms^{-2}$

Question 7: Palette 7/454

Advance Online April 2019 MCQ

A spring whose unstretched length is $l$ has a force constant $k$ . The spring is cut into two pieces of unstretched lengths $l_{1}$ and $l_{2}$ where, $l_{1} = nl_{2}$ and $n$ is an integer. The ratio $\frac{k_1}{k_2}$ of the corresponding force constants, $k_{1}$ and $k_{2}$ will be

A

$n^2$

B

$\frac{1}{n^2}$

C

$n$

D

$\frac{1}{n}$

Question 8: Palette 8/454

Advance Online April 2019 MCQ

A smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $\omega^{2}$ is equal to

A

$\frac{(g\sqrt{3})}{r}$

B

$\frac{2g}{r}$

C

$\frac{2g}{(r\sqrt{3})}$

D

$\frac{\sqrt{3}g}{2r}$

Question 9: Palette 9/454

Advance Online January 2019 MCQ

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (Take $g = 10 \, ms^{-2}$ )

A

25 N

B

32 N

C

18 N

D

23 N

Question 10: Palette 10/454

Advance Online January 2019 MCQ

A mass of $10\mathrm{kg}$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the roof at some point, the rope deviated at an angle of $45^{\circ}$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is $(g = 10\mathrm{ms}^{-2})$

A

$100\mathrm{N}$

B

$200\mathrm{N}$

C

$70\mathrm{N}$

D

$140\mathrm{N}$

Question 11: Palette 11/454

Advance Online January 2019 MCQ

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is

A

$\sqrt{\frac{2k}{p}}$

B

$2\sqrt{\frac{p}{k}}$

C

$\sqrt{\frac{2p}{k}}$

D

$2\sqrt{\frac{k}{p}}$

Question 12: Palette 12/454

Advance Online January 2019 MCQ

A particle moves from the point $(2.0\hat{i}+4.0\hat{j})$ m, at t=0, with an initial velocity $(5.0\hat{i}+4.0\hat{j})$ ms $^{-1}$ . It is acted upon by a constant force which produces a constant acceleration $(4.0\hat{i}+4.0\hat{j})$ ms $^{-2}$ . What is the distance of the particle from the origin at time 2 s?

A

$20\sqrt{2}$ m

B

15 m

C

$10\sqrt{2}$ m

D

5 m

Question 13: Palette 13/454

Advance Online January 2019 MCQ

A block kept on a rough inclined plane, as shown in the figure, remains at rest up to a maximum force $2\mathrm{N}$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\mathrm{N}$ . The coefficient of static friction between the block and the plane is [Take $g = 10~\mathrm{ms}^{-2}$ ]

A

$\frac{1}{2}$

B

$\frac{\sqrt{3}}{2}$

C

$\frac{\sqrt{3}}{4}$

D

$\frac{2}{3}$

Question 14: Palette 14/454

Advance 2018 MCQ

Two masses $m_{1}=5$ kg and $m_{2}=10$ kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight $m$ that should be put on top of $m_2$ to stop the motion is

A

$18.3\mathrm{kg}$

B

$27.3\mathrm{kg}$

C

$43.3\mathrm{kg}$

D

$10.3\mathrm{kg}$

Question 15: Palette 15/454

Advance Online 2018 MCQ

A given object takes n times more time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is

A

$\sqrt{1-\frac{1}{n^{2}}}$

B

$1-\frac{1}{n^{2}}$

C

$\frac{1}{2-n^{2}}$

D

$\sqrt{\frac{1}{1-n^{2}}}$

Question 16: Palette 16/454

Advance Online 2018 MCQ

A body of mass 2 kg slides down with an acceleration of $3 \, ms^{-2}$ on a rough inclined plane having a slope of $30^{\circ}$ . The external force required to take the same body up the plane with the same acceleration will be $(g = 10 \, \text{ms}^{-2})$

A

6 N

B

14 N

C

4 N

D

20 N

Question 17: Palette 17/454

Advance Online 2017 MCQ

Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in the figure. They collide completely inelastically and move as a single particle $C$ . The angle $\theta$ that the path, $C$ makes with the X-axis is given by

A

$\tan\theta=\frac{\sqrt{3}+\sqrt{2}}{1-\sqrt{2}}$

B

$\tan\theta=\frac{1-\sqrt{3}}{1+\sqrt{2}}$

C

$\tan\theta=\frac{\sqrt{3}-\sqrt{2}}{1-\sqrt{2}}$

D

$\tan\theta=\frac{1-\sqrt{2}}{\sqrt{2}(1+\sqrt{3})}$

Question 18: Palette 18/454

Advance Online 2017 MCQ

A conical pendulum of length 1 m makes an angle $\theta = 45^{\circ}$ w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be (Take $g = 10 \, ms^{-2}$ )

A

$0.4\mathrm{ms}^{-1}$

B

$2\mathrm{ms}^{-1}$

C

$0.2\mathrm{ms}^{-1}$

D

$4\mathrm{ms}^{-1}$

Question 19: Palette 19/454

Advance Online 2016 MCQ

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $\mu_{min}$ between the mass and the inclined surface such that the mass does not move is

A

$\tan2\theta$

B

$\tan\theta$

C

$3\tan\theta$

D

$2\tan\theta$

Question 20: Palette 20/454

Advance Online 2016 MCQ

A particle of mass m is acted upon by a force F given by the empirical law $F = \frac{R}{t^{2}} v(t)$ . If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot (A) $\log v(t)$ against $\frac{1}{t}$

A

$\log v(t)$ against $\frac{1}{t}$

B

$v(t)$ against $t^{2}$

C

$\log v(t)$ against $\frac{1}{t^{2}}$

D

$\log v(t)$ against t

Question 21: Palette 21/454

Advance JEE (Advanced) 2016 MCQ

A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth, vertical wall of height $h(

A

$\frac {h}{l} = \frac {\sqrt {3}}{1 6}, f = \frac {1 6 \sqrt {3}}{3} \mathrm{N}$

B

$\frac {h}{l} = \frac {3}{1 6}, f = \frac {1 6 \sqrt {3}}{3} \mathrm{N}$

C

$\frac{h}{l}=\frac{3\sqrt{3}}{16},\quad f=\frac{8\sqrt{3}}{3},\text{N}$

D

$\frac{h}{l}=\frac{3\sqrt{3}}{16},\quad f=\frac{16\sqrt{3}}{3},\text{N}$

Question 22: Palette 22/454

Advance 2015 MCQ

Given in the figure are two blocks $A$ and $B$ of weight $20\mathrm{N}$ and $100\mathrm{N}$ , respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is 0.1 and between block $B$ and the wall is 0.15, the frictional force applied by the wall on block $B$ is

A

$120\mathrm{N}$

B

$150\mathrm{N}$

C

$100\mathrm{N}$

D

$80\mathrm{N}$

Question 23: Palette 23/454

Advance Online 2015 MCQ

A block of mass m = 10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed v, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height H, then neglecting energy losses and taking $g = 10 \, ms^{-2}$ , the value of H is close to

A

0.2 km

B

0.3 km

C

0.04 km

D

0.5 km

Question 24: Palette 24/454

Advance Online 2015 MCQ

A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length $L(L \gg r)$ and are at rest at random positions. The rod is mounted between two rigid supports (shown in figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic)

A

$\frac{mv^2}{L - nr}$

B

$\frac{mv^2}{L - 2nr}$

C

$\frac{mv^2}{2(L - nr)}$

D

zero

Question 25: Palette 25/454

Advance 2014 MCQ

A block of mass m is placed on a surface with a vertical cross section given by $y = \frac{x^{3}}{6}$ . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is

A

$\frac{1}{2}m$

B

$\frac{1}{6}m$

C

$\frac{2}{3}m$

D

$\frac{1}{3}m$

Question 26: Palette 26/454

Advance JEE (Advanced) 2014 Match the Columns

A block of mass $m_{1}=1$ kg another mass $m_{2}=2$ kg are placed together (shown in figure) on an inclined plane with angle of inclination $\theta$ . Various values of $\theta$ are given in Column-I. The coefficient of friction between the block $m_{1}$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_{2}$ and the plane are equal to $\mu=0.3$ .




In Column-II expressions for the friction on the block $m_{2}$ are given. Match the correct expression of the friction in Column-II with the angles given in Column-I and choose the correct option. The acceleration due to gravity is denoted by g.

(Useful information $\tan(5.5^{\circ})\approx0.1$ ; $\tan(11.5^{\circ})\approx0.2$ ; $\tan(16.5^{\circ})\approx0.3$ )

Column-I	Column-II
(P) $\theta = 5^\circ$ (Q) $\theta = 10^\circ$ (R) $\theta = 15^\circ$ (S) $\theta = 20^\circ$	(I) $m_2g\sin\theta$ (II) $(m_1+m_2)g\sin\theta$ (III) $\mu m_2g\cos\theta$ (IV) $\mu(m_1+m_2)g\cos\theta$

A

P-1, Q-1, R-1, S-3

B

P-2, Q-2, R-2, S-3

C

P-2, Q-2, R-2, S-4

D

P-2, Q-2, R-3, S-3

Question 27: Palette 27/454

Advance JEE (Advanced) 2014 MSQ

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_{1}$ and that between the floor and the ladder is $\mu_{2}$ . The normal reaction of the wall on the ladder is $N_{1}$ and that of the floor is $N_{2}$ . If the ladder is about to slip, then

A

$\mu_{1} = 0, \mu_{2} \neq 0$ and $N_{2}\tan \theta = \frac{mg}{2}$

B

$\mu_{1} \neq 0$ , $\mu_{2} = 0$ and $N_{1} \tan \theta = \frac{mg}{2}$

C

$\mu_{1} \neq 0, \mu_{2} \neq 0$ and $N_{2} = \frac{mg}{1 + \mu_{1}\mu_{2}}$

D

$\mu_{1} = 0, \mu_{2} \neq 0$ and $N_{1}\tan \theta = \frac{mg}{2}$

Question 28: Palette 28/454

Advance 2012 MCQ

Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ , respectively. Their speeds are such that they make complete circles in the same time $t$ . The ratio of their centripetal acceleration is

A

$m_{1}:m_{2}$

B

$r_{1}:r_{2}$

C

1:1

D

$m_{1}r_{1}:m_{2}r_{2}$

Question 29: Palette 29/454

Advance IIT-JEE 2012 MSQ

A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle $\theta$ with the horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure. The block remains stationary if (take $g = 10 \, ms^{-2}$ )

A

$\theta = 45^{\circ}$ .

B

$\theta > 45^{\circ}$ and a frictional force acts on the block towards P.

C

$\theta > 45^{\circ}$ and a frictional force acts on the block towards Q.

D

$\theta < 45^{\circ}$ and a frictional force acts on the block towards $Q$ .

Question 30: Palette 30/454

Advance IIT-JEE 2011 MCQ

A ball of mass (m) 0.5 kg is attached to the end of a string having length (l) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rads $^{-1}$ ) is

A

9

B

18

C

27

D

36

Question 31: Palette 31/454

Advance 2010 MCQ

Two fixed frictionless inclined planes making an angle $30^{\circ}$ and $60^{\circ}$ with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

A

$4.9 \, ms^{-2}$ in vertical direction

B

$4.9 \, ms^{-2}$ in horizontal direction

C

$9.8 \, ms^{-2}$ in vertical direction

D

zero

Question 32: Palette 32/454

Advance IIT-JEE 2010 MCQ

A block of mass m is on an inclined plane of angle $\theta$ . The coefficient of friction between the block and the plane is $\mu$ and $\tan\theta > \mu$ . The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from $P_{1} = mg(\sin\theta - \mu\cos\theta)$ to $P_{2} = mg(\sin\theta + \mu\cos\theta)$ , the frictional force f versus P graph will look like

A

B

C

D

Question 33: Palette 33/454

Advance IIT-JEE 2009 MCQ

A piece of wire is bent in the shape of a parabola $y = kx^{2}$ (y-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration $a$ . The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is

A

$\frac{a}{gk}$

B

$\frac{a}{2gk}$

C

$\frac{2a}{gk}$

D

$\frac{a}{4gk}$

Question 34: Palette 34/454

Advance JEE (Advanced) 2008 MCQ

Statement-I: It is easier to pull a heavy object than to push it on a level ground. Statement-II: The magnitude of frictional force depends on the nature of the two surfaces in contact.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 35: Palette 35/454

Advance IIT-JEE 2007 MCQ

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$ . The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$ . As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x$ , is

A

$\frac{F}{2m}\frac{a}{\sqrt{a^2 - x^2}}$

B

$\frac{F}{2m}\frac{x}{\sqrt{a^2 - x^2}}$

C

$\frac{F}{2m}\frac{x}{a}$

D

$\frac{F}{2m}\frac{\sqrt{a^2 - x^2}}{x}$

Question 36: Palette 36/454

Advance JEE (Advanced) 2007 MCQ

Statement-I: A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table. Statement-II: For every action there is an equal and opposite reaction.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 37: Palette 37/454

Advance IIT-JEE 2006 MCQ

System shown in figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass 2m and m just after the string is cut will be

A

$\frac{g}{2}$ upwards, $g$ downwards

B

g upwards, $\frac{g}{2}$ downwards

C

g upwards, 2g downwards

D

2g upwards, g downwards

Question 38: Palette 38/454

Advance IIT-JEE 2005 MCQ

A block of mass m is at rest under the action of force F against a wall as shown in figure. Which of the following statement is incorrect?

A

$f = mg$ [where $f$ is the frictional force]

B

$F = N$ [where $N$ is the normal force]

C

F will not produce torque

D

N will not produce torque

Question 39: Palette 39/454

Advance IIT-JEE 2004 MCQ

A block P of mass m is placed on a horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks?

A

$\frac{kA}{2}$

B

$kA$

C

$\mu_{s}mg$

D

zero

Question 40: Palette 40/454

Advance IIT-JEE 2003 MCQ

The maximum value of the force F such that the block shown in the arrangement, does not move is

A

$20\mathrm{N}$

B

$10\mathrm{N}$

C

$12\mathrm{N}$

D

$15\mathrm{N}$

Question 41: Palette 41/454

Advance IIT-JEE 2001 MCQ

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 42: Palette 42/454

Advance IIT-JEE 2001 MCQ

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by

A

$\sqrt{2}Mg$

B

$\sqrt{2}mg$

C

$\sqrt{(M + m)^2 + m^2} g$

D

$\sqrt{(M+m)^{2}+M^{2}}g$

Question 43: Palette 43/454

Advance IIT-JEE 2001 MCQ

An insect crawls up a hemispherical surface very slowly as shown in figure. The coefficient of friction between the surface and the insect is $\frac{1}{3}$ . If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by

A

$\cot \alpha = 3$

B

$\tan \alpha = 3$

C

$\sec \alpha = 3$

D

$\csc \alpha = 3$

Question 44: Palette 44/454

Advance IIT-JEE 2001 MCQ

A small block is shot into each of the four tracks as shown in the figure. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

A

B

C

D

Question 45: Palette 45/454

Advance 2000 MSQ

An engine of mass $5 \times 10^{4}$ kg pulls a coach of mass $4 \times 10^{4}$ kg. A resistance of 1 N per 100 kg is acting on both the coach and the engine and if the driving force of the engine is 4500 N then

A

the acceleration of the system (coach + engine) is $0.04 \, ms^{-2}$ .

B

the acceleration of the system (coach + engine) is $0.05 \, ms^{-2}$ .

C

the tension in the coupling is 2000 N.

D

the tension in the coupling is 2400 N.

Question 46: Palette 46/454

Advance 2000, 2M MCQ

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with a constant angular acceleration $\alpha$ . If the coefficient of friction between the rod and the bead is $\mu$ , and gravity is neglected, then the time after which the bead starts slipping is

A

$\sqrt{\frac{\mu}{\alpha}}$

B

$\frac{\mu}{\sqrt{\alpha}}$

C

$\frac{1}{\sqrt{\mu\alpha}}$

D

infinitesimal

Question 47: Palette 47/454

Advance IIT-JEE 1994 MCQ

A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.5, then the magnitude of frictional force acting on the block is

A

2.5 N

B

0.98 N

C

4.9 N

D

0.49 N

Question 48: Palette 48/454

Advance IIT-JEE 1992 MCQ

A car is moving in a circular horizontal track of radius 10 m with a constant speed of $10 \, ms^{-1}$ . A plumb bob is suspended from the roof of the car by a light rigid rod of length 1 m. The angle made by the rod with the track is

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 49: Palette 49/454

Advance IIT-JEE 1990 MCQ

When a bicycle is in motion and pedalled, the force of friction exerted by ground on the two wheels is such that it acts

A

In the backward direction on the front wheel and in the forward direction on the rear wheel.

B

In the forward direction on the front wheel and in the backward direction on the rear wheel.

C

In the backward direction on both the front and the rear wheels.

D

In the forward direction on both the front and the rear wheels.

Question 50: Palette 50/454

Advance IIT-JEE 1986 MSQ

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits $-\phi$ and $+\phi$ . For an angular displacement $\theta(|\theta|<\phi)$ , the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions

A

$T \cos \theta = Mg$

B

$T - Mg \cos \theta = \frac{MV^{2}}{L}$

C

The magnitude of the tangential acceleration of the bob $\left|a_{T}\right|=g\sin\theta.$

D

$T = Mg \cos \theta$

Question 51: Palette 51/454

Advance IIT-JEE 1986 MSQ

A reference frame attached to the earth

A

is an inertial frame by definition.

B

cannot be an inertial frame because of revolution of earth round the sun.

C

is an inertial frame because Newton's laws are applicable in this frame.

D

cannot be an inertial frame because of rotation of earth about its own axis.

Question 52: Palette 52/454

Advance IIT-JEE 1980 MCQ

A block of mass 2 kg rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is

A

9.8 N

B

$0.7 \times 9.8$ N

C

$9.8 \times \sqrt{3}$ N

D

$0.7 \times 9.8 \times \sqrt{3}$ N

Question 53: Palette 53/454

Advance IIT-JEE 1980 MCQ

A ship of mass $3 \times 10^{7}$ kg, initially at rest, is pulled by a force of $5 \times 10^{4}$ N through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is

A

$1.5 \, ms^{-1}$

B

$60 \, ms^{-1}$

C

$0.1 \, ms^{-1}$

D

$5 \, ms^{-1}$

Question 54: Palette 54/454

Advance MCQ

A body of mass 2 kg is moving towards east with a uniform speed of $2 \, ms^{-1}$ . A force of 3 N is applied to it towards north. The magnitude of the displacement of the body 2 s after the application of force is

A

4 m

B

5 m

C

6 m

D

7 m

Question 55: Palette 55/454

Advance MCQ

A block of mass m, is placed on an inclined plane of mass M moving towards right horizontally with an acceleration $a_{0} = g$ . The length of the plane AC = 1 m. Friction is absent everywhere. The time taken by the block to reach C starting from A is $(g = 10 \, \text{ms}^{-2})$

A

0.42 s

B

0.74 s

C

1.2 s

D

2.56 s

Question 56: Palette 56/454

Advance MCQ

Two masses each equal to m are lying on x-axis at $(-a, 0)$ and $(+a, 0)$ , respectively, as shown in figure. They are connected by a light string. A force F is applied at the origin along vertical direction. As a result the masses move towards each other without loosing contact with ground. The acceleration of each mass at the instant when the masses are at $(-x, 0)$ and $(x, 0)$ respectively is

A

$\frac{2F}{m}\frac{\sqrt{a^{2}-x^{2}}}{x}$

B

$\frac{2F}{m}\frac{x}{\sqrt{a^2 - x^2}}$

C

$\frac{F}{2m}\frac{x}{\sqrt{a^2 - x^2}}$

D

$\frac{F}{m}\frac{x}{\sqrt{a^2 - x^2}}$

Question 57: Palette 57/454

Advance MCQ

A particle of mass M is attached to the lower end of a vertical rope of mass m. An upward force P acts on the upper end of the rope. The system is free to move. The force exerted by the rope on the block is $\frac{PM}{M+m}$

A

only if the rope is uniform

B

in gravity-free space only

C

only if $P > (M + m)g$

D

in all cases

Question 58: Palette 58/454

Advance MCQ

A log of weight W is pulled at a constant velocity and with a force F by means of a rope of length L. The distance between the free end of the rope and the ground is h. Neglecting the thickness of the log the coefficient of friction between the log and the ground is

A

$\mu=\frac{F\sqrt{L^{2}-h^{2}}}{WL-Fh}$

B

$\mu=\frac{\sqrt{L^{2}-h^{2}}}{WL-Fh}$

C

$\mu=\frac{WL-Fh}{F\sqrt{L^{2}-h^{2}}}$

D

$\mu=\frac{WL-Fh}{\sqrt{L^{2}-h^{2}}}$

Question 59: Palette 59/454

Advance MCQ

Three identical rigid circular cylinders A, B and C are arranged on smooth inclined surfaces as shown in figure. The least value of $\theta$ that prevents the arrangement from collapsing is

A

$\tan^{-1}\left(\frac{1}{2}\right)$

B

$\tan^{-1}\left(\frac{1}{2\sqrt{3}}\right)$

C

$\tan^{-1}\left(\frac{1}{3\sqrt{3}}\right)$

D

$\tan^{-1}\left(\frac{1}{4\sqrt{3}}\right)$

Question 60: Palette 60/454

Advance MCQ

The greatest height h of the sand pile that can be erected without spilling the sand onto the surrounding circular area of radius R (if $\mu$ is the coefficient of friction between sand particles) is

A

R

B

$\frac{R}{\mu}$

C

$\mu R$

D

$\mu^{2}R$

Question 61: Palette 61/454

Advance MCQ

In the arrangement shown in figure, coefficient of friction between the two blocks is $\mu = \frac{1}{2}$ . The force of friction acting between the two blocks is

A

4 N

B

6 N

C

8 N

D

10 N

Question 62: Palette 62/454

Advance MCQ

A bead of mass m is fitted on a rod and can move on it without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a horizontal plane with an acceleration $a_{0}$ in a direction forming an $\alpha$ with the rod. The acceleration of bead with respect to rod is

A

$g\sin \alpha$

B

$(g + a_0)\sin \alpha$

C

$g\sin \alpha +a_{0}\cos \alpha$

D

$g\sin \alpha -a_0\cos \alpha$

Question 63: Palette 63/454

Advance MCQ

A block of mass 10 kg lies on a rough inclined plane of inclination $\theta=\sin^{-1}\left(\frac{3}{5}\right)$ with the horizontal when a force of 30 N is applied on the block parallel to and upward the plane, the total force exerted by the plane on the block is nearly along $\left(\text{coefficient of friction is }\mu=\frac{3}{4}\right)\quad\left(g=10\mathrm{~ms}^{-2}\right)$

A

OA

B

OB

C

OC

D

OD

Question 64: Palette 64/454

Advance MCQ

A block of mass 10 kg lies on a rough inclined plane of inclination $\theta=\sin^{-1}\left(\frac{3}{5}\right)$ with the horizontal when a force of 30 N is applied on the block parallel to and upward the plane, the acceleration of the block is

A

$3 \, ms^{-2}$ up the plane

B

$3 \, ms^{-2}$ down the plane

C

$6 \, ms^{-2}$ up the plane

D

zero

Question 65: Palette 65/454

Advance MCQ

A ball of mass $m$ is thrown upward with a velocity $v$ . If air exerts an average resisting force $F$ , the velocity with which the ball returns to the thrower is

A

$v\sqrt{\frac{mg}{mg + F}}$

B

$v\sqrt{\frac{F}{mg + F}}$

C

$v\sqrt{\frac{mg - F}{mg + F}}$

D

$v\sqrt{\frac{mg + F}{mg - F}}$

Question 66: Palette 66/454

Advance MCQ

In the arrangement shown in figure $m_A = m_B = 2$ kg. String is massless and pulley is frictionless. Block $B$ is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is $\mu = 0.5$ . The maximum horizontal force F that can be applied so that block A does not slip over the block B is (take $g = 10 \, ms^{-2}$ ).

A

$25\mathrm{N}$

B

$40\mathrm{N}$

C

$30\mathrm{N}$

D

$20\mathrm{N}$

Question 67: Palette 67/454

Advance MCQ

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 68: Palette 68/454

Advance MCQ

In the arrangement shown, $m_{1}=1$ kg, $m_{2}=2$ kg, the pulleys and strings are ideal and all surfaces in contact are frictionless. The value of M for which the mass $m_{1}$ moves with constant velocity is

A

$6\mathrm{kg}$

B

$4\mathrm{kg}$

C

$8\mathrm{kg}$

D

$10\mathrm{kg}$

Question 69: Palette 69/454

Advance MCQ

In the figure shown the force with which the man should pull the rope to hold the plank in position is F. If weight of the man is 60 kgf, the plank and pulleys have negligible masses, then

A

$F = 150\mathrm{N}$

B

$F = 300\mathrm{N}$

C

$F = 600\mathrm{N}$

D

$F = 1200\mathrm{N}$

Question 70: Palette 70/454

Advance MCQ

In the arrangement shown, acceleration of A is $1 \, ms^{-2}$ upwards, acceleration of B is $7 \, ms^{-2}$ upwards and acceleration of C is $2 \, ms^{-2}$ upwards. Then acceleration of D has to be

A

$7\mathrm{ms}^{-2}$ , downwards

B

$2\mathrm{ms}^{-2}$ , downwards

C

$10\mathrm{ms}^{-2}$ , downwards

D

$8\mathrm{ms}^{-2}$ , downwards

Question 71: Palette 71/454

Advance MCQ

A particle of mass m is joined to a very heavy mass M by a light string passing over a light and frictionless pulley. Both the bodies are then set free. The total thrust on the pulley is

A

mg

B

2mg

C

4mg

D

much greater than mg

Question 72: Palette 72/454

Advance MCQ

The figure represents a light inextensible string ABCDE in which AB = BC = CD = DE and to which are attached masses M, m and M at the points B, C and D, respectively. The system hangs freely in equilibrium with ends A and E of the string fixed in the same horizontal line shown in figure. It is given that $\tan \alpha = \frac{3}{4}$ and $\tan \beta = \frac{12}{5}$ . Then the tension in the string BC is

A

2mg

B

$\frac{13}{10} mg$

C

$\frac{3}{10} mg$

D

$\frac{20}{11} mg$

Question 73: Palette 73/454

Advance MCQ

A block is placed on a rough horizontal plane. A time dependent horizontal force $F = Kt$ acts on the block, where $K$ is a positive constant. The acceleration-time graph of the block is

A

B

C

D

Question 74: Palette 74/454

Advance MCQ

A mass $m_{1}$ , placed on top of a trolley of mass $m_{3}$ , is connected to another mass $m_{2}$ by means of a string passing over a smooth pulley as shown in figure. The friction between surfaces is negligible. For $m_{1}$ and $m_{2}$ not to move with respect to trolley, the horizontal force F to be applied on trolley is

A

$F = m_{3}g$

B

$F = (m_{1} + m_{2})g$

C

$F = \left( m_{1} + m_{2} + m_{3} \right) \frac{m_{2} g}{m_{1}}$

D

$F = m_{1}g$

Question 75: Palette 75/454

Advance MCQ

Same spring is attached with 2 kg, 3 kg and 1 kg blocks in three different cases as shown in figure. If $x_{1}$ , $x_{2}$ and $x_{3}$ be the extensions in the spring in these three cases then

A

$x_{1}=0, x_{3}>x_{2}$

B

$x_{2} > x_{1} > x_{3}$

C

$x_{3} > x_{1} > x_{2}$

D

$x_{1} > x_{2} > x_{3}$

Question 76: Palette 76/454

Advance MCQ

The magnitude of the force (in N) acting on a body varies with time t (in $\mu$ s) as shown in figure. AB, BC and CD are straight line segments. The magnitude of the total impulse of the force on the body from $t = 4 \mu s$ to $t = 16 \mu s$ is

A

$5\times 10^{-3}\mathrm{Ns}$

B

$5\times 10^{-4}\mathrm{Ns}$

C

$5\times 10^{-2}\mathrm{Ns}$

D

$5\times 10^{-1}\mathrm{Ns}$

Question 77: Palette 77/454

Advance MCQ

Blocks A and C start from rest and move to the right with acceleration $a_{A}=12t\ ms^{-2}$ and $a_{C}=3\ ms^{-2}$ . Here t is in second. The time when block B again comes to rest is

A

2 s

B

1 s

C

$\frac{3}{2}\mathrm{s}$

D

$\frac{1}{2}\mathrm{s}$

Question 78: Palette 78/454

Advance MCQ

Two blocks A and B of masses m and M respectively are placed on each other and their combination rests on a fixed horizontal surface C. A light string passing over the smooth light pulley is used to connect A and B as shown. The coefficient of sliding friction between all surfaces in contact is $\mu$ . If A is dragged with a force F then for both A and B to move with a uniform speed have

A

$F = \mu (M + m)g$

B

$F = \mu mg$

C

$F = \mu (3M + m)g$

D

$F = \mu (3m + M)g$

Question 79: Palette 79/454

Advance MCQ

In a horizontal circle of radius R a particle P is rotating with a constant speed v. Another particle Q is moving along the diameter of the circle with a constant acceleration $a = \frac{v^{2}}{R}$ . Net force on P as observed by Q is

A

constant both in magnitude and direction

B

constant in magnitude only

C

zero at least once during one rotation

D

None of these

Question 80: Palette 80/454

Advance MCQ

Sixteen balls of equal masses are connected like beads on a string. Some balls are placed on a smooth inclined plane of inclination $\sin^{-1}\left(\frac{1}{3}\right)$ and the remaining balls hang over the top of the plane. The number of balls hanging so as to produce an acceleration of $\frac{g}{2}$ is

A

8

B

9

C

10

D

11

Question 81: Palette 81/454

Advance MCQ

A block is kept on a smooth inclined plane of angle of inclination $30^{\circ}$ that moves with a constant acceleration so that the block does not slide relative to the inclined plane. Let F be the contact force between the block and the plane. Now the inclined plane stops and let f be the contact force between the two in this case. Then $\frac{F}{f}$ is

A

1

B

$\frac{4}{3}$

C

2

D

$\frac{3}{2}$

Question 82: Palette 82/454

Advance MCQ

A box is put on a scale which is adjusted to read zero when the box is empty. A stream of pebbles is then poured into the box from a height h above its bottom at a rate of n pebbles per second. Each pebble has a mass m. If the pebbles collide with the box such that they immediately come to rest after collision. Then the scale reading at time t after the pebbles begin to fill the box is

A

mngt

B

$mn\sqrt{2gh}$

C

mg

D

$mn\left(\sqrt{2gh}+gt\right)$

Question 83: Palette 83/454

Advance MCQ

A horizontal force F is applied on a very light rod inserted between the two identical blocks A and B placed over a rough surface as shown in figure. If the force F is gradually increased, then which of the blocks will move first?

A

$A$

B

$B$

C

both move simultaneously

D

This depends on the friction coefficient between the blocks and the ground

Question 84: Palette 84/454

Advance MCQ

An inclined plane makes an angle $30^{\circ}$ with the horizontal. A groove OA = 5 m cut in the plane makes an angle $30^{\circ}$ with OX. A short smooth body is free to slide down the influence of gravity. The time taken by the body to reach from A to O is $(g = 10 \, \text{ms}^{-2})$

A

4 s

B

2 s

C

$2\sqrt{2}\mathrm{s}$

D

1 s

Question 85: Palette 85/454

Advance MCQ

In the arrangement shown, the wall is smooth, but the surfaces of blocks $A$ and $B$ in contact are rough. In the state of equilibrium, the force of friction on $B$ due to $A$ is

A

zero

B

upwards

C

downwards

D

such that the system cannot stay in equilibrium

Question 86: Palette 86/454

Advance MCQ

An elevator accelerates upward at a constant rate. A uniform string of length L and mass m supports a small block of mass M that hangs from the ceiling of an elevator which accelerates upwards at a constant rate. The tension at distance l from the ceiling is T. The acceleration of the elevator is

A

$\frac{T}{\left(2M+m-\frac{ml}{L}\right)}+g$

B

$\frac{T}{\left(2M-m+\frac{ml}{L}\right)}-g$

C

$\frac{T}{\left(M+m-\frac{ml}{L}\right)}-g$

D

$\frac{T}{\left(M+\frac{ml}{L}\right)}-g$

Question 87: Palette 87/454

Advance MCQ

A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination $30^{\circ}$ with horizontal. Acceleration of train up the plane is $a_0 = \frac{g}{2}$ . The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is

A

$30^{\circ}$

B

$\tan^{-1}\left(\frac{2}{\sqrt{3}}\right)$

C

$\tan^{-1}\left(\frac{\sqrt{3}}{2}\right)$

D

$\tan^{-1}

Question 88: Palette 88/454

Advance MCQ

A solid sphere will be in stable equilibrium when its centre of gravity lies

A

vertically above its centre

B

vertically below its centre

C

on the horizontal line through its centre

D

none of the above

Question 89: Palette 89/454

Advance MCQ

Two masses $m$ and $M$ are attached with strings as shown. For the system to be in equilibrium have

A

$\tan \theta = 1 + \frac{2M}{m}$

B

$\tan \theta = 1 + \frac{2m}{M}$

C

$\tan \theta = 1 + \frac{M}{2m}$

D

$\tan \theta = 1 + \frac{m}{2M}$

Question 90: Palette 90/454

Advance MCQ

In the system shown in figure $m_{B}=4$ kg, and $m_{A}=2$ kg. The pulleys are massless and friction is absent everywhere. The acceleration of block A is $(g=10\ \mathrm{ms}^{-2})$

A

$\frac{10}{3}\mathrm{ms}^{-2}$

B

$\frac{20}{3}\mathrm{ms}^{-2}$

C

$2\mathrm{ms}^{-2}$

D

$4\mathrm{ms}^{-2}$

Question 91: Palette 91/454

Advance MCQ

In the arrangement shown the pulleys and the strings are ideal. The respective accelerations of the blocks A and B are

A

$g, \frac{g}{2}$

B

$\frac{g}{2}, g$

C

$\frac{3g}{2}, \frac{3g}{4}$

D

$g, g$

Question 92: Palette 92/454

Advance MCQ

Beads A and B, each of mass m, are connected by a light inextensible cord. They are constrained (restricted) to move on a frictionless ring in a vertical plane as shown. The beads are released from rest at the positions shown. The tension in the cord just after the release is

A

$\sqrt{2} mg$

B

$mg$

C

$\frac{mg}{\sqrt{2}}$

D

$2mg$

Question 93: Palette 93/454

Advance MCQ

Two unequal masses are connected by a light inex-tensible string which passes over a frictionless light pulley. After the system has moved from rest for 3 s, the string is cut. If the lighter mass ascends $\frac{49}{90}$ m before it begins to descend and the heavier mass is 5 kg then the lighter mass is

A

4 kg

B

3 kg

C

10 kg

D

12 kg

Question 94: Palette 94/454

Advance MCQ

A block $A$ of mass $m$ is placed over a plank $B$ of mass $2m$ . Plank $B$ is placed over a smooth horizontal surface. The coefficient of friction between $A$ and $B$ is $\frac{1}{2}$ . Block $A$ is given a velocity $v_{0}$ towards right. Acceleration of $B$ relative to $A$ is

A

$\frac{g}{2}$

B

$g$

C

$\frac{3g}{4}$

D

zero

Question 95: Palette 95/454

Advance MCQ

An automobile enters a turn whose radius is $R$ . The road is banked at angle $\theta$ . Friction is negligible between wheels of the automobile and road. Mass of the automobile is $m$ and speed is $v$ . Select the correct alternative

A

net force on the automobile is zero

B

normal reaction on the automobile is $mg\cos\theta$

C

normal reaction on the automobile is $mg\sec\theta$

D

net force on the automobile is $\sqrt{(mg)^2 + \left(\frac{mv^2}{R}\right)^2}$

Question 96: Palette 96/454

Advance MCQ

Three blocks A, B and C of equal mass m are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of A, B and C is $\frac{1}{2}$ and that between C and ground is zero. The maximum value of mass of block D so that the blocks A, B and C move without slipping over each other is

A

$3\mathrm{m}$

B

$4\mathrm{m}$

C

$5\mathrm{m}$

D

$6\mathrm{m}$

Question 97: Palette 97/454

Advance MCQ

A block of mass m=4 kg is placed over a rough inclined plane having coefficient of friction $\mu=0.6$ as shown in figure. A force F=10 N is applied on the block at an angle of $30^{\circ}$ . The contact force between the block and the plane is

A

10.65 N

B

16.32 N

C

27.15 N

D

32.16 N

Question 98: Palette 98/454

Advance MCQ

On a fixed wedge, two blocks A and B are placed as shown. The coefficient of friction between the block A of mass m and block B of mass 2m is $\mu$ . There is no friction between block B and the inclined plane. If the system of blocks A and B is released from rest, then for no slipping between A and B, have

A

$\theta \leq \cos^{-1}(2\mu)$

B

$2\theta \leq \tan^{-1}\left(\frac{\mu}{2}\right)$

C

$2\theta \leq \tan^{-1}(2\mu)$

D

$\theta \leq \tan^{-1}(\mu)$

Question 99: Palette 99/454

Advance MCQ

In the arrangement shown, two bodies of mass $m$ and $4m$ are attached with string. The body of mass $m$ hanging from the string of length $l$ is executing oscillations of angular amplitude $\theta_0$ while the other body is at rest. The minimum coefficient of friction between the mass $4m$ and the horizontal surface is

A

$\mu_{\mathrm{MIN}}=\left(\frac{2-\cos\theta_{0}}{3}\right)$

B

$\mu_{\mathrm{MIN}} = 2\cos^2\left(\frac{\theta_0}{2}\right)$

C

$\mu_{\mathrm{MIN}} = \left(\frac{3 - \cos\theta_0}{4}\right)$

D

$\mu_{\mathrm{MIN}} = \left(\frac{3 - 2\cos\theta_0}{4}\right)$

Question 100: Palette 100/454

Advance MCQ

The system shown in figure is released from rest. The spring gets elongated (Neglect friction and masses of pulley, string and spring)

A

if $M > m$

B

if $M > 2m$

C

if $M > \frac{m}{2}$

D

for any value of $M$

Question 101: Palette 101/454

Advance MCQ

Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in figure. The system is released from rest. The larger mass is stopped for a moment, 1 second after the system is set into motion. The time elapsed before the string is tight again is $(g = 10\mathrm{ms}^{-2})$

A

$\frac{1}{4}$ s

B

$\frac{1}{2}$ s

C

$\frac{2}{3}s$

D

$\frac{1}{3}s$

Question 102: Palette 102/454

Advance MCQ

Given $m_{A} = 30 \, kg$ , $m_{B} = 10 \, kg$ , $m_{C} = 20 \, kg$ . Between A and B $\mu_{1} = 0.3$ , between B and C $\mu_{2} = 0.2$ and between C and ground $\mu_{3} = 0.1$ . The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown in figure is $(g = 10 \, \text{ms}^{-2})$

A

60 N

B

90 N

C

80 N

D

150 N

Question 103: Palette 103/454

Advance MCQ

A car going at a speed of $6 \, ms^{-1}$ encounters an incline (inclination angle $30^{\circ}$ ) of length 15 m. The friction coefficient between the road and tyres is 0.5. The minimum speed of car with which it can reach the bottom is $\left(g = 10 \, \text{ms}^{-2}\right)$

A

$10 \, ms^{-1}$

B

$7.5 \, ms^{-1}$

C

$5 \mathrm{ms} ^ {- 1}$

D

$2.5 \, ms^{-1}$

Question 104: Palette 104/454

Advance MCQ

In order to raise a block of mass $100\mathrm{kg}$ a man of mass $60\mathrm{kg}$ fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $\frac{5g}{4}$ relative to rope. The tension in the rope is $(g = 10\mathrm{ms}^{-2})$

A

$1432\mathrm{N}$

B

$928\mathrm{N}$

C

$1218\mathrm{N}$

D

$642\mathrm{N}$

Question 105: Palette 105/454

Advance MCQ

A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes an angle of $30^{\circ}$ with the ground. A monkey of mass 5 kg climbs up the rope. The clamp can tolerate a vertical force of 40 N only. The maximum acceleration in upward direction with which the monkey can climb safely is (Neglect friction and take $g = 10 \, ms^{-2}$ )

A

$2 \mathrm{ms} ^ {- 2}$

B

$4 \, ms^{-2}$

C

$6 \mathrm{ms} ^ {- 2}$

D

$8 \, ms^{-2}$

Question 106: Palette 106/454

Advance MCQ

A block of mass 15 kg is resting on a rough inclined plane as shown in figure. The block is tied up by a horizontal string which has a tension of 50 N. The coefficient of friction between the surfaces of contact is $(g = 10 \, \text{ms}^{-2})$

A

$\frac{1}{2}$

B

$\frac{2}{3}$

C

$\frac{3}{4}$

D

$\frac{1}{4}$

Question 107: Palette 107/454

Advance MCQ

In the arrangement shown in figure, pulley is smooth and massless and all the strings are light. Let $F_{1}$ be the force exerted on the pulley in CASE-1 and $F_{2}$ the force in CASE-2. Then

A

$F_{1} > F_{2}$

B

$F_{1} < F_{2}$

C

$F_{1}=F_{2}$

D

$F_{1}=2F_{2}$

Question 108: Palette 108/454

Advance MCQ

A block of mass m is placed on a rough horizontal plane attached with an elastic spring of spring constant k as shown in figure. Initially spring is unstretched. If the plane is now gradually lifted from $\theta = 0^{\circ}$ to $\theta = 90^{\circ}$ , then the graph showing extension in the spring (x) versus angle ( $\theta$ ) is

A

B

C

D

Question 109: Palette 109/454

Advance MCQ

The maximum value of mass of block C so that neither A nor B moves is (Given that mass of A is 100 kg and that of B is 140 kg. Pulleys are smooth and friction coefficient between A and B and between B and horizontal surface is $\mu = 0.3$ ) $g = 10 \, ms^{-2}$

A

210 kg

B

190 kg

C

185 kg

D

162 kg

Question 110: Palette 110/454

Advance MCQ

A homogeneous chain of length $L$ lies on a table. The coefficient of friction between the chain and the table is $\mu$ . The maximum length which can hang over the table in equilibrium is (The vertical portion of table is smooth)

A

$\left(\frac{\mu}{\mu + 1}\right)L$

B

$\left(\frac{1 - \mu}{\mu}\right)L$

C

$\left(\frac{1 - \mu}{1 + \mu}\right)L$

D

$\left(\frac{2\mu}{2\mu + 1}\right)L$

Question 111: Palette 111/454

Advance MCQ

Consider the arrangement shown. Suppose all the surfaces are rough, the direction of friction on $B$ due to $A$ , on $A$ due to wall and on $A$ due to $B$ is

A

up, down, up

B

up, up, down

C

down, up, up

D

depends on the masses of A and B and friction coefficients at different surfaces

Question 112: Palette 112/454

Advance MCQ

A block of mass m slides down an inclined plane of inclination $\theta$ with uniform speed. The coefficient of friction between the block and the plane is $\mu$ . The contact force between the block and the plane is

A

$mg\sin\theta\sqrt{1+\mu^{2}}$

B

$\sqrt{(mg\sin\theta)^{2}+(\mu mg\cos\theta)^{2}}$

C

$mg\sin\theta$

D

mg

Question 113: Palette 113/454

Advance MCQ

A block of mass m = 2 kg is at rest on a rough inclined plane of inclination $30^{\circ}$ as shown. The coefficient of friction between the block and the plane is $\mu = 0.5$ . The minimum force F that must be applied on the block perpendicular to the plane, so that block does not slip on the plane is $(g = 10 \, \text{ms}^{-2})$

A

zero

B

6.24 N

C

2.68 N

D

4.34 N

Question 114: Palette 114/454

Advance MCQ

On a plank of mass 2 kg, length 1.25 m lying on a smooth horizontal ground, a block of mass 1 kg is placed. The coefficient of friction between the block and the plank is 0.5. A constant force F = 35 N is applied on the plank in horizontal direction. The time after which the block will separate from the plank is $(g = 10 \, \text{ms}^{-2})$

A

0.25 s

B

0.5 s

C

1 s

D

2 s

Question 115: Palette 115/454

Advance MCQ

A body slides down an inclined plane of inclination $\theta$ . The coefficient of friction down the plane varies in direct proportion to the distance moved down the plane as $\mu = kx$ , where k is a constant. The body will move down the plane with a

A

constant acceleration $g \sin \theta$ .

B

constant acceleration $g(\sin\theta - \mu\cos\theta)$ .

C

variable acceleration $g(\mu \sin \theta - \cos \theta)$ .

D

variable acceleration first decreasing from $g \sin \theta$ to zero and then becoming negative.

Question 116: Palette 116/454

Advance MCQ

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by

A

$\sqrt{2}Mg$

B

$\sqrt{2}mg$

C

$\left[\sqrt{(M+m)^{2}+m^{2}}\right]g$

D

$\left[\sqrt{(M + m)^2 + M^2}\right]g$

Question 117: Palette 117/454

Advance MCQ

A small particle of mass m is released from rest from point A inside a smooth hemispherical bowl as shown in figure. The ratio $(x)$ of magnitude of centripetal force and normal reaction on the particle at any point B varies with $\theta$ as

A

B

C

D

Question 118: Palette 118/454

Advance MCQ

Three freight cars of mass M are pulled with force F by a locomotive. Friction is negligible. The ratio of the forces on each car from the end where F is applied is

A

3:2:1

B

1:2:3

C

1:1:1

D

3:1:2

Question 119: Palette 119/454

Advance MCQ

A particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec{a} = (4\hat{i} + 3\hat{j})\mathrm{ms}^{-2}$ and $\vec{p} = (8\hat{i} - 6\hat{j})\mathrm{kgms}^{-1}$ . The motion of the particle is

A

accelerated circular motion

B

de-accelerated circular motion

C

uniform circular motion

D

data insufficient to say anything with $\vec{a}$ and $\vec{p}$ only

Question 120: Palette 120/454

Advance MCQ

Assuming the gravity to be in negative z-direction, a force $\vec{F} = \vec{v} \times \vec{A}$ is exerted on a particle in addition to the force of gravity where $\vec{v}$ is the velocity of the particle and $\overline{A}$ is a constant vector in positive x-direction. The minimum speed $\vec{v}_{min}$ with which a particle of mass m must be projected so that it continues to move undeflected with constant velocity is

A

$\vec{v}_{\min} = -\frac{A}{mg}\hat{j}$

B

$\vec{v}_{\min} = \frac{A}{mg}\hat{j}$

C

$\vec{v}_{\min} = \frac{mg}{A}\hat{j}$

D

$\vec{v}_{\min} = -\frac{mg}{A}\hat{j}$

Question 121: Palette 121/454

Advance MCQ

Two masses m and M are connected by a light string passing over a smooth pulley. When set free m moves up by 1.4 m in 2 s. The ratio $\frac{m}{M}$ is

A

$\frac{13}{15}$

B

$\frac{15}{13}$

C

$\frac{9}{7}$

D

$\frac{7}{9}$

Question 122: Palette 122/454

Advance MCQ

An airplane requires for take-off a speed of $80 \, kmh^{-1}$ , the run on the ground being 100 m. The mass of the airplane is 10,000 kg and the coefficient of friction between the airplane and the ground is 0.2. Assuming that the plane accelerates uniformly during take-off, the minimum force required by the engine for take-off is

A

$2 \times 10^{4}$ N

B

$2.43 \times 10^{4}$ N

C

$4.43 \times 10^{4}$ N

D

$8.86 \times 10^{4}$ N

Question 123: Palette 123/454

Advance MCQ

In the pulley arrangement shown, the pulley $P_{2}$ is movable. Assuming coefficient of friction between $m$ and surface to be $\mu$ , the minimum value of $M$ for which $m$ is at rest is

A

$M = \frac{\mu m}{2}$

B

$m = \frac{\mu M}{2}$

C

$M = \frac{m}{2\mu}$

D

$m = \frac{M}{2\mu}$

Question 124: Palette 124/454

Advance MCQ

A block is gently dropped on a conveyor belt moving at $3 \, ms^{-1}$ . If the coefficient of friction between the belt and the block is 0.5. The displacement of block relative to the conveyor belt before the slipping between the two is stopped ( $g = 10 \, ms^{-2}$ )

A

0.9 m

B

1.2 m

C

1.8 m

D

2.7 m

Question 125: Palette 125/454

Advance MCQ

A block of mass m is held on a rough inclined plane by a spring parallel to the plane as shown. The natural length of the spring is $l_{0}$ and its force constant is $\lambda$ . The frictional force is in magnitude proportional to the speed of the block. If l be the equilibrium length, then

A

$l = l_{0} \left( 1 + \frac{2mg \sin \alpha}{\lambda} \right)$

B

$l = l_{0} \left( 1 + \frac{mg \sin \alpha}{\lambda} \right)$

C

$l = l_{0} \left( 1 - \frac{2mg \sin \alpha}{\lambda} \right)$

D

$l = l_{0} \left( 1 - \frac{mg \sin \alpha}{\lambda} \right)$

Question 126: Palette 126/454

Advance MCQ

A car starts from rest to cover a distance of $500\mathrm{m}$ on a road whose coefficient of friction with the tyres of the car is $\frac{1}{2}$ . The minimum time in which the car can cover this distance is $(g = 10\mathrm{ms}^{-2})$

A

$5\mathrm{s}$

B

$10\mathrm{s}$

C

$20\mathrm{s}$

D

$40\mathrm{s}$

Question 127: Palette 127/454

Advance MCQ

A particle of mass $m$ moving with velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$ . They are in contact for a very brief time $T$ . Their force of interaction increases from zero to $F_0$ linearly in time $\frac{T}{2}$ , and decreases linearly to zero in a further time $\frac{T}{2}$ . The magnitude of $F_0$ is

A

$\frac{mu}{2T}$

B

$\frac{mu}{T}$

C

$\frac{2mu}{T}$

D

None of these

Question 128: Palette 128/454

Advance MCQ

Two blocks $M$ and $m$ are arranged as shown in the figure. The coefficient of friction between the blocks $M$ and $m$ is $\mu_{1} = 0.25$ and between the ground and $M$ is $\mu_{2} = \frac{1}{3}$ . If $M = 8\mathrm{kg}$ , then the value of $m$ for which the system will remain at rest is

A

$\frac{4}{3}$ kg

B

$\frac{8}{9}$ kg

C

1 kg

D

$\frac{8}{5}$ kg

Question 129: Palette 129/454

Advance MCQ

Two blocks of masses $m_1$ and $m_2$ are connected with a light spring and placed over a plank moving with an acceleration $a$ as shown in figure. The coefficient of friction between the blocks and plank is $\mu$ . The spring will

A

neither be compressed nor be stretched for $a \leq \mu g$

B

be compressed if $a \leq \mu g$

C

be stretched if $a > \mu g$

D

be in its natural length under all conditions

Question 130: Palette 130/454

Advance MCQ

A block is about to slide down an inclined plane when its angle to the horizontal is $\theta$ . If now an another block of same mass is put on the block

A

it will not slide down the plane unless the inclination is increased

B

it can remain in equilibrium even if the inclination is slightly decreased

C

it will about to slide when the inclination is greater than $\frac{\theta}{2}$

D

it is still about to slide down the plane

Question 131: Palette 131/454

Advance MCQ

In CASE-1, the wedge B is stationary and block A starts sliding when the angle of plane is greater than $\theta$ , while in CASE-2, the wedge B is moving upwards with an acceleration $a_{0}$ and the block A starts sliding when the angle of plane is greater than $\alpha$ . The coefficient of friction between A and B in both the cases is same. Then CASE-I CASE-II

A

$\frac{\tan\theta}{\tan\alpha}=\frac{g}{a_{0}}$

B

$\theta < \alpha$

C

$\theta >\alpha$

D

$\theta = \alpha$

Question 132: Palette 132/454

Advance MCQ

Two spheres of equal masses are attached to a string of length $2\mathrm{m}$ as shown. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant rate. If $T_{1}$ is the tension in the string between $P \& Q$ and $T_{2}$ is the tension in the string between $P \& O$ then $\frac{T_1}{T_2}$ equals

A

1

B

$\frac{1}{3}$

C

$\frac{2}{3}$

D

$\frac{1}{2}$

Question 133: Palette 133/454

Advance MCQ

A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination $\alpha$ with acceleration $a_{0}$ is

A

$\theta = \tan^{-1}\alpha$

B

$\theta = \tan^{-1}\left(\frac{a_0}{g}\right)$

C

$\theta=\tan^{-1}\left(\frac{g}{a_{0}}\right)$

D

$\theta=\tan^{-1}\left(\frac{a_{0}+g\sin\alpha}{g\cos\alpha}\right)$

Question 134: Palette 134/454

Advance MCQ

A car is moving in a circular horizontal track of radius 10 m with a constant speed of $10 \, ms^{-1}$ . A plumb bob is suspended from the roof of the car by a light rigid rod of length 1 m. The angle made by the rod with the track is

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 135: Palette 135/454

Advance MCQ

A block is placed on a rough inclined plane having inclination angle $\theta$ . Now, the angle $\theta$ is increased from $0^{\circ}$ to $90^{\circ}$ , then the contact force between the block and the plane

A

remains constant

B

first increases then decreases

C

first decreases then increases

D

first remains constant then decreases

Question 136: Palette 136/454

Advance MCQ

A particle of mass $m$ , initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T$ . It begins to move with a velocity $u$ after the force stops acting. $F$ is shown in the graph as a function of time. The curve is an ellipse

A

$u = \frac{\pi F_0^2}{2m}$

B

$u = \frac{\pi T^2}{8m}$

C

$u = \frac{\pi F_0T}{4m}$

D

$u = \frac{F_0T}{2m}$

Question 137: Palette 137/454

Advance MCQ

A ball of mass 1 kg is released from position A inside a wedge which has a hemispherical cut of radius 0.5 m as shown. Assuming all surfaces to be smooth, the force exerted by the vertical wall OM on wedge, when the ball is in position B is $g = 10 \, \text{ms}^{-2}$

A

$5\sqrt{3}\mathrm{N}$

B

$10\mathrm{N}$

C

$\frac{15\sqrt{3}}{2}\mathrm{N}$

D

$15\mathrm{N}$

Question 138: Palette 138/454

Advance MCQ

A bar of mass m resting on a smooth horizontal plane starts moving due to a force $F = \frac{mg}{3}$ of constant magnitude. In the process of its rectilinear motion, the angle $\theta$ between the direction of this force and the horizontal varies as $\theta = ks$ , where k is a constant and s is the displacement of the particle. The velocity of bar as a function of $\theta$ is

A

$v = \sqrt{\frac{2g}{3}\sin\theta}$

B

$v = \sqrt{\frac{2g}{3k}\cos\theta}$

C

$v = \sqrt{\frac{2g}{3k}\sin\theta}$

D

$v = \sqrt{\frac{2g}{3}\cos\theta}$

Question 139: Palette 139/454

Advance MCQ

Two small balls each having a radius $R$ , having masses $m_{1}$ and $m_{2}(m_{1} > m_{2})$ , tied by a thin light thread are dropped from a certain height. Taking upward buoyancy force $F$ into account, the tension $T$ in the thread during the flight when the motion of the balls becomes uniform is

A

$\left(m_{1} - m_{2}\right)g$

B

$\left(m_{1}-m_{2}\right)\frac{g}{2}$

C

$(m_{1}+m_{2})g$

D

$\left(m _ {1} + m _ {2}\right) \frac {g}{2}$

Question 140: Palette 140/454

Advance MCQ

On an inclined plane of inclination angle $30^{\circ}$ , a block is placed. It is observed that the force to drag the block along the plane upwards is smaller than the force required to lift it. The maximum value of coefficient of friction is

A

$\frac{\sqrt{3}}{2}$

B

$\frac{1}{2}$

C

$\frac{1}{\sqrt{3}}$

D

$\frac{2}{3}$

Question 141: Palette 141/454

Advance MCQ

In the arrangement shown, the string is light, pulley is smooth, the total mass on left hand side of the pulley is $m_{1}$ , on right hand side is $m_{2}$ , the coefficient of friction between block B and the wedge is $\mu=\frac{1}{2}$ and the inclination angle is $\theta=30^{\circ}$ . Select the incorrect option.

A

Block $B$ will slide down if $m_{1} = m_{2}$

B

Block $B$ may remain stationary with respect to wedge for suitable values of $m_{1}$ and $m_{2}$ with $m_{2} > m_{1}$

C

Block B will slide down if $m_{1} > m_{2}$

D

Block B cannot remain stationary with respect to wedge in any case

Question 142: Palette 142/454

Advance MCQ

A horizontal force $F$ is applied to a block of mass $m$ on a smooth inclined plane of inclination $\theta$ to the horizontal as shown in figure. The resultant force on the block is

A

$F\sin \theta -mg\cos \theta$

B

$F + mg\tan \theta$

C

$F\sin \theta +mg\cos \theta$

D

$F\cos \theta -mg\sin \theta$

Question 143: Palette 143/454

Advance MCQ

A 4 kg block is connected with two springs of force constants $k_{1}=100\ Nm^{-1}$ and $k_{2}=300\ Nm^{-1}$ as shown in figure. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is $(g=10\ ms^{-2})$

A

zero

B

$5\mathrm{ms}^{-2}$ upwards

C

$10\mathrm{ms}^{-2}$ downwards

D

$10\mathrm{ms}^{-2}$ upwards

Question 144: Palette 144/454

Advance MCQ

A man of mass 60 kg is pulling a block of mass M by an inextensible light rope passing through a smooth and massless pulley as shown in figure. The coefficient of friction between the man and the ground is $\mu=\frac{1}{2}$ . The maximum value of M that can be pulled by the man without slipping on the ground is approximately

A

$26\mathrm{kg}$

B

$32\mathrm{kg}$

C

$46\mathrm{kg}$

D

$51\mathrm{kg}$

Question 145: Palette 145/454

Advance MCQ

A wooden block of mass $M$ resting on a rough horizontal floor is pulled with a force $F$ at an angle $\phi$ with the horizontal. If $\mu$ is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

A

$\frac{F}{M}\sin\phi$

B

$\mu F\cos\phi$

C

$\frac{F}{M}(\cos\phi - \mu\sin\phi) - \mu g$

D

$\frac{F}{M}(\cos\phi + \mu\sin\phi) - \mu g$

Question 146: Palette 146/454

Advance MCQ

An electric fan is placed on a stationary boat and air is blown with it on the sail of the boat. Select the correct statement(s) from the following.

A

The boat will start moving with a uniform speed.

B

The boat will be uniformly accelerated in the direction of flow of the air.

C

The boat will be uniformly accelerated opposite to the direction of the flow of air.

D

The boat will remain stationary as before.

Question 147: Palette 147/454

Advance MCQ

In a tug-of-war contest, two teams A and B pull on a horizontal rope from the opposite sides. The winner team will be the one who

A

exerts greater force on the rope.

B

exerts greater force on the ground.

C

exerts a force on the rope greater than the tension existing in the rope.

D

data insufficient to arrive at a result.

Question 148: Palette 148/454

Advance MCQ

A bowl of soup rests on a table in the dining car of a train. If the acceleration of the train is $a_0$ in the forward direction then the angle which the surface of the soup makes with the horizontal is

A

$\arctan\left(\frac{a_0}{g}\right)$

B

$\arctan\left(\frac{g}{a_0}\right)$

C

$\arctan\left(\frac{a_0}{\sqrt{a_0^2 + g^2}}\right)$

D

$\arctan\left(\frac{g}{\sqrt{a_0^2 + g^2}}\right)$

Question 149: Palette 149/454

Advance MCQ

A block of metal weighing 2 kg is resting on a frictionless plane. It is struck by a jet of water at a rate of $1 \, kgs^{-1}$ at a speed of $5 \, ms^{-1}$ . The initial acceleration of the block is

A

$\frac{2}{5} \, ms^{-2}$

B

$\frac{5}{2} \, ms^{-2}$

C

$5 \, ms^{-2}$

D

$\frac{1}{5} \, ms^{-2}$

Question 150: Palette 150/454

Advance MCQ

A particle of mass m moves along the internal smooth surface of a vertical cylinder of radius R as shown. The force which acts on the wall of the cylinder if initially the velocity $v_{0}$ of the particle makes an angle $\alpha$ with the horizontal (Assume that particle does not leave contact with the curved surface of the cylinder) is

A

$\frac{mv_0^2}{R}$

B

$\frac{mv_0^2\cos^2\alpha}{R}$

C

$\frac{mv_0^2\sin^2\alpha}{R}$

D

$mg$

Question 151: Palette 151/454

Advance MCQ

In the figure, the ball B is released from rest when the spring is at its natural length. For the block A of mass 2m to leave contact with the ground at some instant, the minimum mass of B must be

A

$2m$

B

$m$

C

$\frac{m}{2}$

D

$\frac{m}{4}$

Question 152: Palette 152/454

Advance MCQ

A blimp of mass m is descending with an acceleration $a_{0}$ . A buoyant force is acting on the blimp which is equal to the weight of the air displaced by the blimp. Assuming the buoyant force to be constant the ballast that must be jettisioned from the blimp so that it rises with same acceleration $a_{0}$ is

A

$\left(\frac{2g}{g+a_{0}}\right)m$

B

$\left(\frac{2a_{0}}{g}\right)m$

C

$\left(\frac{2a_{0}}{g+a_{0}}\right)m$

D

$\left(\frac{2a_{0}}{g-a_{0}}\right)m$

Question 153: Palette 153/454

Advance MCQ

A car with closed windows takes a left turn. A helium filled balloon in the car will be pushed to the

A

right

B

left

C

front

D

back

Question 154: Palette 154/454

Advance MCQ

According to the basic postulates of the "Theory of Relativity", the laws of Physics are same in

A

all frames of reference.

B

Only those frames of reference which move at constant velocity with respect to an inertial frame.

C

only those frames of reference which move at constant acceleration with respect to an inertial frame.

D

only those frames which rotate with constant angular velocity with respect to an inertial frame.

Question 155: Palette 155/454

Advance MCQ

A string with constant tension T is deflected through an angle $2\theta_{0}$ by a smooth fixed pulley. The force on the pulley is

A

$2T \cos \theta_{0}$

B

$T \cos \theta_{0}$

C

$2T \sin \theta_{0}$

D

$T \sin \theta_{0}$

Question 156: Palette 156/454

Advance MCQ

A man running along a straight road leans a little in the forward direction. The angle between the vertical line and the line joining the man's centre of gravity with the point of support is $\theta_0$ . For the man not to slip, the coefficient of friction satisfies the condition given by

A

$\mu \leq \tan \theta_0$

B

$\mu \geq \tan \theta_0$

C

$\mu \geq \tan^2\theta_0$

D

$\mu \leq \tan^2\theta_0$

Question 157: Palette 157/454

Advance MCQ

Vertically hanging curtains between the compartments in an airplane are seen to bend forward. This indicates that the airplane is

A

taking off

B

moving steadily at constant altitude

C

slowing down for landing

D

taking a bend

Question 158: Palette 158/454

Advance MCQ

A particle of mass m rests on a horizontal floor with which it has a coefficient of static friction $\mu$ . For the block to just move

A

A minimum force $F_{\min} = \frac{\mu mg}{\sqrt{1 + \mu^{2}}}$ has to be applied at an angle $\theta = \tan^{-1}\left(\frac{1}{\mu}\right)$ with the horizontal.

B

A minimum force $F_{\mathrm{min}} = \mu mg$ has to be applied at an angle $\theta = \tan^{-1}(\mu)$ with the horizontal.

C

A minimum force $F_{\min} = \frac{\mu mg}{\sqrt{1 + \mu^2}}$ has to be applied at an angle $\theta = \tan^{-1}(\mu)$ with the horizontal.

D

A minimum force $F_{\mathrm{min}} = \mu mg$ has to be applied at an angle $\theta = \tan^{-1}\left(\frac{1}{\mu}\right)$ with the horizontal.

Question 159: Palette 159/454

Advance MCQ

A prism of mass $M$ is placed on a horizontal surface. A block of mass $m$ slides on it, which in turn slides on the horizontal surface. Assume all surfaces to be frictionless the acceleration of the block with respect to the prism is

A

$g\sin \theta$

B

$g\cos \theta$

C

$\left(\frac{M + m}{M + m\sin^2\theta}\right) g\sin \theta$

D

$\left(\frac{M + m}{M + m\sin^2\theta}\right) g\cos \theta$

Question 160: Palette 160/454

Advance MCQ

A body slides over an inclined plane forming an angle of $45^{\circ}$ with the horizontal. The distance x travelled by the body in time t is described by the equation $x = kt^{2}$ , where k = 1.732. The coefficient of friction between the body and the plane has a value

A

$\mu = 0.5$

B

$\mu = 1$

C

$\mu = 0.25$

D

$\mu = 0.75$

Question 161: Palette 161/454

Advance MCQ

The inclined plane shown in figure has an acceleration $\vec{a}_{0}$ to the right. If $\mu_{s} = \tan\theta$ is the coefficient of static friction for all surfaces in contact. The block will slide on the plane for

A

$a _ {0} > g \tan \theta$

B

$a_0 < g \tan \theta$

C

$a_{0} > g \tan(\theta - \alpha)$

D

$a_0 < g \tan (\theta - \alpha)$

Question 162: Palette 162/454

Advance MCQ

A board of mass m is placed on the floor and a man of mass M is standing on the board as shown. The coefficient of friction between the board and the floor is $\mu$ . The maximum force that the man can exert on the rope so that the board does not slip on the floor is

A

$F = \mu (M + m)g$

B

$F = \mu mg$

C

$F = \frac{\mu Mg}{\mu + 1}$

D

$F = \frac{\mu(M + m)g}{\mu + 1}$

Question 163: Palette 163/454

Advance MCQ

A body rests on a rough horizontal plane. A force is applied to the body directed towards the plane at an angle $\phi$ with the vertical. If $\theta$ is the angle of friction then for the body to move along the plane

A

$\phi >\theta$

B

$\phi < \theta$

C

$\phi = \theta$

D

$\phi$ can take up any value

Question 164: Palette 164/454

Advance MCQ

The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If $\phi$ is angle of friction and $\theta$ is the angle which incline makes with the horizontal then,

A

$\tan \theta = \tan \phi$

B

$\tan \theta = 2\tan \phi$

C

$\tan \theta = 3\tan \phi$

D

$\tan \phi = 3\tan \theta$

Question 165: Palette 165/454

Advance MCQ

The system is pushed by a force $F$ as shown in figure. All surfaces are smooth except between $B$ and $C$ . Friction coefficient between $B$ and $C$ is $\mu$ . Minimum value of $F$ to prevent block $B$ from downward slipping is

A

$\left(\frac{3}{2\mu}\right)mg$

B

$\left(\frac{5}{2\mu}\right)mg$

C

$\left(\frac{5}{2}\right)\mu mg$

D

$\left(\frac{3}{2}\right)\mu mg$

Question 166: Palette 166/454

Advance MCQ

In the arrangement shown, blocks $A$ and $B$ connected with an inextensible string move with velocities $v_{1}$ and $v_{2}$ along horizontal direction. The ratio of $\frac{v_2}{v_1}$ is

A

$\frac{\sin\alpha}{\sin\beta}$

B

$\frac{\sin\beta}{\sin\alpha}$

C

$\frac{\cos\beta}{\cos\alpha}$

D

$\frac{\cos\alpha}{\cos\beta}$

Question 167: Palette 167/454

Advance MCQ

In the arrangement shown, the block A moves left with an acceleration of $6 \, ms^{-2}$ , such that at all the instants, the block B always remains horizontal. The acceleration of B is

A

$6\mathrm{ms}^{-2}$

B

$4\mathrm{ms}^{-2}$

C

$2\mathrm{ms}^{-2}$

D

$1\mathrm{ms}^{-2}$

Question 168: Palette 168/454

Advance MCQ

Springs of spring constant $K$ , $3K$ , $9K$ , $27K$ , ..., $\infty$ are connected in series. The equivalent spring constant of the combination is

A

$\frac{3K}{2}$

B

$\frac{K}{2}$

C

$\frac{2K}{3}$

D

$\infty$

Question 169: Palette 169/454

Advance MCQ

Two blocks of masses 4 kg and 10 kg are connected by flexible inextensible string as shown. The pulley is assumed to be light and frictionless. The coefficient of friction between the 4 kg block and the surface is 0.2 and angle of inclination of the plane is $30^{\circ}$ . Assume the system to be released from rest, the velocity of 10 kg block when it has moved 4 m down is

A

$6.5\mathrm{ms}^{-1}$

B

$5.6\mathrm{ms}^{-1}$

C

$41.8\mathrm{ms}^{-1}$

D

$13\mathrm{ms}^{-1}$

Question 170: Palette 170/454

Advance MCQ

A block $A$ is placed over a long rough plank $B$ of same mass as shown in figure. The plank is placed over a smooth horizontal surface. At time $t = 0$ , block $A$ is given a velocity $v_{0}$ in horizontal direction. Let $v_{1}$ and $v_{2}$ be the velocities of $A$ and $B$ at time $t$ . Then the correct graph between $v_{1}$ or $v_{2}$ and $t$ is

A

B

C

D

Question 171: Palette 171/454

Advance MCQ

A block B is placed on block A. The mass of block B is less than the mass of block A. Friction exists between the blocks, whereas the ground on which the block A is placed is taken to be smooth. A horizontal force F, increasing linearly with time begins to act on B. The acceleration $a_{A}$ and $a_{B}$ of blocks A and B respectively are plotted against t. The correctly plotted graph is

A

B

C

D

Question 172: Palette 172/454

Advance MCQ

A mass m is drawn up a smooth inclined plane of height h and length l by means of a string passing over a pulley fixed at the vertex of the plane as shown. A mass M hangs from the other end. For m to just reach the top of the plane, $M$ must be detached when $m$ has moved through a distance

A

$\frac{mh}{M}$

B

$\frac{ml}{M}$

C

$\frac{M}{M+m}\left(\frac{hl}{h+l}\right)$

D

$\frac{M + m}{M}\left(\frac{hl}{h + l}\right)$

Question 173: Palette 173/454

Advance MCQ

In the arrangement shown, if the blocks $A$ and $B$ move towards each other with acceleration values $a$ and $b$ , respectively, then acceleration of the block $C$ is

A

$2a + 2b$

B

$\sqrt{4a^2 + 5b^2 + 8ab}$

C

a

D

$\sqrt{5a^2 + 4b^2 + 8ab}$

Question 174: Palette 174/454

Advance MCQ

A car starts from rest to cover a distance $s$ . The coefficient of friction between the road and the tyres is $\mu$ . The minimum time in which the car can cover the distance $s$ is proportional to

A

$\frac{1}{\mu}$

B

$\frac{1}{\sqrt{\mu}}$

C

$\mu$

D

$\sqrt{\mu}$

Question 175: Palette 175/454

Advance MCQ

In the shown arrangement if $f_{1}$ , $f_{2}$ and T be the frictional forces on 2 kg block, 3 kg block and tension in the string respectively, then their values are

A

2 N, 6 N, 3.2 N

B

2N, 6N, 0N

C

1N, 6N, 2N

D

Data insufficient to calculate the required values

Question 176: Palette 176/454

Advance MCQ

In the figure given below, if all surface are assumed to be smooth and the force $F = 100 \mathrm{~N}$ . If acceleration of block $B$ of mass $20 \mathrm{~kg}$ is $a$ and tension in string connecting block $A$ of mass $20 \mathrm{~kg}$ is $T$ then just after when the force $F$ is applied

A

T = 0 and $a = 5 \, ms^{-2}$

B

$T = 100\mathrm{N}$ and $a = 0$

C

$T = 200\mathrm{N}$ and $a = 5\mathrm{ms}^{-2}$

D

None of these

Question 177: Palette 177/454

Advance MCQ

The block of mass m is placed on a rough horizontal floor and it is pulled by an ideal string as shown by a constant force F. As the block moves towards right the friction force on block

A

remains constant

B

increases

C

decreases

D

can be said

Question 178: Palette 178/454

Advance MCQ

Two blocks each of mass 20 kg are connected by an ideal string and this system is kept on rough horizontal surface as shown. Initially the string is just tight then a horizontal force F = 120 N is applied on one block as shown. If friction coefficient at every contact is $\mu = 0.5$ then which of the following represents the correct free body diagram.

A

B

C

D

All of the above

Question 179: Palette 179/454

Advance MCQ

A particle is moving along a circular path with a constant speed. The acceleration of the particle is constant in

A

magnitude

B

direction

C

both magnitude and direction

D

neither magnitude nor direction

Question 180: Palette 180/454

Advance MCQ

A particle moves in $x - y$ plane. The position vector of particle at any time $t$ is $\vec{r} = \left[(2t)\hat{i} + (2t^2)\hat{j}\right]\mathrm{m}$ . The rate of change of $\theta$ at time $t = 2\mathrm{s}$ . (where $\theta$ is the angle which its velocity vector makes with positive $x$ -axis) is

A

$\frac{2}{17}$ rads $^{-1}$

B

$\frac{1}{14}$ rads $^{-1}$

C

$\frac{4}{7}$ rads $^{-1}$

D

$\frac{6}{5}$ rads $^{-1}$

Question 181: Palette 181/454

Advance MCQ

Two identical ideal springs of spring constant $1000 \, Nm^{-1}$ are connected by a pulley as shown in figure and this arrangement is established in the vertical plane. The pulley is ideal and string passing over pulley is massless. At equilibrium of pulley $\theta$ is $60^{\circ}$ and the masses $m_{1}$ and $m_{2}$ are 2 kg and 3 kg, respectively. Then the elongation in each spring when $\theta = 60^{\circ}$ is

A

$1.6\sqrt{3}\mathrm{cm}$

B

$1.6\mathrm{cm}$

C

$4.8\mathrm{cm}$

D

None of these

Question 182: Palette 182/454

Advance MCQ

A sphere of mass m is held between two smooth inclined walls A and B. For $\sin(37^{\circ})=\frac{3}{5}$ , the normal reaction of the wall (2) is equal to

A

mg

B

$mg \sin(74^{\circ})$

C

$mg \cos(74^{\circ})$

D

None of these

Question 183: Palette 183/454

Advance MCQ

A block A of mass 2 kg rests on another block B of mass 8 kg which rests on a horizontal floor. The coefficient of friction between A and B is 0.2 while between B and floor is 0.5. When a horizontal force $25\mathrm{N}$ is applied on $B$ , the frictional force acting between $A$ and $B$ is

A

$0\mathrm{N}$

B

$3.9\mathrm{N}$

C

$5\mathrm{N}$

D

$49\mathrm{N}$

Question 184: Palette 184/454

Advance MCQ

A block starts moving up a fixed inclined plane of inclination $60^{\circ}$ with a velocity of $20\mathrm{ms}^{-1}$ and stops after 2 s. The approximate value of coefficient of friction is $(g = 10\mathrm{ms}^{-2})$

A

3

B

3.3

C

0.27

D

0.33

Question 185: Palette 185/454

Advance MCQ

A point on the periphery of rotating disc has its acceleration vector making on angle $30^{\circ}$ with velocity vector then the ratio of magnitude of centripetal acceleration to tangential acceleration is

A

$\sin (30^{\circ})$

B

$\cos (30^{\circ})$

C

$\tan (30^{\circ})$

D

None of these

Question 186: Palette 186/454

Advance MCQ

Find the only correct statement from the following statements

A

A body has a constant velocity and still it can have a varying speed

B

A body has a constant speed but it can have a varying velocity

C

A body having constant speed cannot have any acceleration

D

A body in motion under a force acting upon it must always have work done upon it

Question 187: Palette 187/454

Advance MCQ

A smooth sphere of radius $R$ and mass $M$ is placed on the smooth horizontal floor. Another smooth particle of mass $m$ is placed on the sphere and a horizontal force $F$ is applied on the sphere as shown. If the particle does not slip on the sphere then the value of force $F$ is

A

$F = mg\cot \theta$

B

$F = Mg\cot \theta$

C

$F = (m + M)g \cot \theta$

D

$F = (m + M)g\tan \theta$

Question 188: Palette 188/454

Advance MCQ

The contact force exerted by a body on another body is perpendicular to the surfaces in contact. Then,

A

the surfaces in contact must be frictionless

B

the force of friction between the bodies may not be zero

C

the contact force equals the normal reaction

D

the contact force equals the friction

Question 189: Palette 189/454

Advance MCQ

A rod AB of mass 10 kg tied with a string at C such that AC = BC and rod remains in equilibrium then friction force by horizontal surface will be

A

50 N towards right

B

50 N towards left

C

100 N

D

None of these

Question 190: Palette 190/454

Advance MCQ

A block of mass m is moving on a rough horizontal surface where coefficient of friction between block and surface is $\mu=0.5$ . At t=0, block is moving with a velocity $\vec{v}$ . Then a horizontal force F=2t is applied on it in the direction of velocity, where t represents time, then the speed of block after the application of force

A

decreases

B

increases

C

first decreases then increases

D

first increases then decreases

Question 191: Palette 191/454

Advance MCQ

A circular disc of radius r = 5 m is rotating in horizontal plane about y-axis. y-axis a vertical axis passing through the centre of disc and x-z is the horizontal plane at ground. The height of disc above ground is h = 5 m. Small particles are ejecting from disc in horizontal direction with speed $12 \, ms^{-1}$ from the circumference of disc then the distance of these particles from origin when they hits x-z plane is

A

5 m

B

12 m

C

13 m

D

None of these

Question 192: Palette 192/454

Advance MCQ

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A tip of the propeller breaks off when the propeller is vertical. At that instant, the period of the motion of the propeller is 1.2 second. The fragment files off horizontally, falls and strikes the ground at point P. In figure, the distance from the base of the pylon to the point where the fragment strikes the ground is closest to

A

120 m

B

130 m

C

140 m

D

160 m

Question 193: Palette 193/454

Advance MCQ

Two blocks A and B of masses m and 2m, respectively are held at rest such that the string is in natural length. Find out the accelerations of both the blocks just after release.

A

$g \downarrow, g \downarrow$

B

$\frac{g}{3} \downarrow, \frac{g}{3} \uparrow$

C

0, 0

D

$g \downarrow, 0$

Question 194: Palette 194/454

Advance MCQ

In the arrangement shown, the wedge of mass $M$ moves towards left with an acceleration $a$ . All surfaces are smooth. The acceleration of mass $m$ relative to wedge is

A

$\frac{a}{2}$

B

$\frac{2Ma}{m}$

C

$\frac{2(M + m)a}{m}$

D

$\frac{(M + m)a}{m}$

Question 195: Palette 195/454

Advance MCQ

A body $A$ rests on $B$ and friction coefficient between $A$ and $B$ is $\mu$ . Block $M$ is placed on a frictionless surface. Then (i) (ii)

A

the maximum possible value of $F$ so that both bodies move together in case (i) is $\mu(m+M)g$

B

the maximum possible value of F so that both bodies move together in case (i) is $\mu mg$

C

the maximum possible value of $F$ so that both bodies move together in case (ii) is $\mu(M+m)g$

D

the maximum possible value of $F$ so that both bodies move together in case (ii) is $\mu Mg$

Question 196: Palette 196/454

Advance MCQ

A bicycle is in motion. When it is not pedalled, the force of friction exerted by the ground on two wheels is such that it acts

A

in the backward direction on the front wheel and in the forward direction on the rear wheel

B

in the forward direction on the front wheel and in the backward direction on rear wheel

C

in the backward direction on both the front and the rear wheels

D

in the forward direction on both the front and the rear wheels

Question 197: Palette 197/454

Advance MCQ

A particle is moving in a circular path and its acceleration vector is making an angle of $30^{\circ}$ with the velocity vector, then the ratio of centripetal acceleration to its tangential acceleration is

A

$\frac{1}{2}$

B

$\frac{\sqrt{3}}{2}$

C

$\frac{1}{\sqrt{3}}$

D

$\sqrt{3}$

Question 198: Palette 198/454

Advance MCQ

A body is moving is x-y plane as shown in a circular path of radius 2 m. At a certain instant when the body is crossing the positive y-axis its acceleration is $(6\hat{i}-8\hat{j})\mathrm{ms}^{-2}$ . Then its angular acceleration and angular velocity at this instant will be

A

$-3\hat{k}$ rads $^{-2}$ and $-2\hat{k}$ rads $^{-1}$ respectively

B

$+3\hat{k}$ rads $^{-2}$ and $+2\hat{k}$ rads $^{-1}$ respectively

C

$-4\hat{k}$ rads $^{-2}$ and $-\sqrt{3}\hat{k}$ rads $^{-1}$ respectively

D

$+4\hat{k}$ rads $^{-2}$ and $+\sqrt{3}\hat{k}$ rads $^{-1}$ respectively

Question 199: Palette 199/454

Advance MCQ

A block of mass m is attached to an ideal spring and system lies in vertical plane as shown. Initially the supporting plane is placed so that spring remains in its natural length then the plane is moved very slowly downwards. The graph showing variation of normal reaction applied by mass on supporting plane with distance travelled by block is

A

B

C

D

None of these

Question 200: Palette 200/454

Advance MCQ

Two identical heavy spheres of equal mass are placed on smooth cup of radius $3r$ , where $r$ is radius of each sphere as shown. Then the ratio of reaction force between cup and any sphere to reaction force between two sphere is

A

1

B

2

C

3

D

None of these

Question 201: Palette 201/454

Advance MCQ

In the given figure, the coefficient of friction between $m_{1}$ and $m_{2}$ is $\mu$ and $m_{2}$ and horizontal surface is zero

A

If $F > \mu m_1g$ , then relative acceleration is found between $m_1$ and $m_2$

B

If $F < \mu m_1g$ , then no relative acceleration is found between $m_1$ and $m_2$

C

If $F > \mu m_{1}g$ , then both bodies move together

D

A and B are correct

Question 202: Palette 202/454

Advance MCQ

The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is $\mu$ . The inclination $\theta$ of the plane is

A

$\tan^{-1}(\mu)$

B

$\tan^{-1}\left(\frac{\mu}{2}\right)$

C

$\tan^{-1}(2\mu)$

D

$\tan^{-1}(3\mu)$

Question 203: Palette 203/454

Advance MCQ

A circular tube of radius R and cross-sectional radius $r(r \ll R)$ is filled completely with iron balls of radius $\rho$ . Iron balls are just fitting into the tubes. The tension in the tube when it is rotated about its axis perpendicular to its plane with angular velocity $\omega$ is

A

$\frac{4}{3}\pi\rho\omega^{2}r^{3}R$

B

$\frac{4}{3}\pi\rho\omega^{2}r^{2}R^{2}$

C

$\frac{2}{3}\pi\rho\omega^{2}r^{3}R$

D

$\frac{2}{3}\pi\rho\omega^{2}r^{2}R^{2}$

Question 204: Palette 204/454

Advance MCQ

A plumb-line is set up on a rotating disk and makes an angle of $\alpha$ with the vertical, as in figure. The distance $r$ from the point of suspension to the axis of rotation is known, and so is the length $l$ of the thread. The angular velocity of rotation is

A

$\omega = \sqrt{\frac{g\tan\alpha}{r + l\sin\alpha}}$

B

$\omega = \sqrt{\frac{g\sin\alpha}{r + l\tan\alpha}}$

C

$\omega = \sqrt{\frac{g}{r + l\sin\alpha}}$

D

$\omega = \sqrt{\frac{g\cos\alpha}{r + l\sin\alpha}}$

Question 205: Palette 205/454

Advance MCQ

The force exerted by the ideal string on the ideal pulley $P$ is

A

mg

B

2mg

C

$\sqrt{2}mg$

D

4mg

Question 206: Palette 206/454

Advance MCQ

A rope of mass $M$ is hanged from two supports $A$ and $B$ as shown in figure. Maximum and minimum tension in the rope respectively are

A

$\frac{Mg\cos\theta_2}{\sin(\theta_1 + \theta_2)},\frac{Mg\cos\theta_1}{\sin(\theta_1 + \theta_2)}$

B

Mg, $Mg\cos\theta_{1}$

C

$\frac{Mg\cos\theta_{2}}{\sin\left(\theta_{1}+\theta_{2}\right)}$ , $\frac{Mg\cos\theta_{1}\cos\theta_{2}}{\sin\left(\theta_{1}+\theta_{2}\right)}$

D

$\frac{Mg\cos\theta_{2}}{\cos(\theta_{2}-\theta_{1})}$ , $\frac{Mg\cos\theta_{1}}{\sin(\theta_{1}+\theta_{2})}$

Question 207: Palette 207/454

Advance MCQ

Three blocks are arranged as shown in which ABCD is a horizontal plane. Strings are massless and both pulley stands vertical while the strings connecting blocks $m_{1}$ and $m_{2}$ are also vertical and are perpendicular to faces AB and BC which are mutually perpendicular to each other. If $m_{1}$ and $m_{2}$ are 3 kg and 4 kg respectively. Coefficient of friction between the block $m_{3}=10$ kg and surface is $\mu=0.6$ , then, frictional force on $m_{3}$ is

A

$30\mathrm{N}$

B

$40\mathrm{N}$

C

$50\mathrm{N}$

D

$60\mathrm{N}$

Question 208: Palette 208/454

Advance MCQ

A block $A$ is placed over a long rough plank $B$ of same mass as shown in figure. The plank is placed over a smooth horizontal surface. At time $t = 0$ , block $A$ is given a velocity $v_{0}$ in horizontal direction. Let $v_{1}$ and $v_{2}$ be the velocities of $A$ and $B$ at time $t$ . Then choose the correct graph between $v_{1}$ or $v_{2}$ and $t$

A

B

C

$$<br /> v _ {1} \text { or } v _ {2}<br /> $$

D

$v_{1}$ or $v_{2}$

Question 209: Palette 209/454

Advance MCQ

Which of the following correctly describes the centripetal acceleration vector for a particle moving in a circular path?

A

Constant and always perpendicular to the velocity vector for the particle

B

Constant and always parallel to the velocity vector for the particle

C

Of constant magnitude and always perpendicular to the velocity for the particle

D

Of constant magnitude and always parallel to the velocity vector for the particle

Question 210: Palette 210/454

Advance MCQ

A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{2}{\pi}$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

A

ML

B

2ML

C

4ML

D

16ML

Question 211: Palette 211/454

Advance MCQ

A block of mass m is slipping down a rough inclined wedge kept at rest on a horizontal table, with constant velocity. Force on wedge by the table is

A

less than $(m+M)g$

B

equal to $(m+M)g$

C

equal to $\left(M + m\cos^2\theta\right)g$

D

will make some non-zero angle with vertical direction

Question 212: Palette 212/454

Advance MCQ

All surface are frictionless and pulley and strings are light. Acceleration of block of mass m is

A

$\frac{2}{5}g$

B

$\frac{4g}{5}$

C

$\frac{4g}{7}$

D

$\frac{2g}{7}$

Question 213: Palette 213/454

Advance MCQ

Block A is placed over the block B as shown in figure. Wedge is smooth and fixed. Force of friction on block A is

A

towards right

B

towards left

C

zero

D

always kinetic

Question 214: Palette 214/454

Advance MCQ

A parabolic bowl with its bottom at origin has the shape $y = \frac{x^{2}}{20}$ . Here x and y are in metre. The maximum height at which a small mass m can be placed on the bowl without slipping (coefficient of static friction is 0.5) is

A

$2.5\mathrm{m}$

B

$1.25\mathrm{m}$

C

$1\mathrm{m}$

D

$4\mathrm{m}$

Question 215: Palette 215/454

Advance MCQ

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5 \, ms^{-1}$ . The height of the plane of circle from vertex of the funnel is

A

0.25 cm

B

2 cm

C

4 cm

D

2.5 cm

Question 216: Palette 216/454

Advance MCQ

The minimum velocity (in ms $^{-1}$ ) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

A

60

B

30

C

15

D

25

Question 217: Palette 217/454

Advance MCQ

A bunch of bananas hangs from the end of a rope that passes over a light, frictionless pulley. A monkey of mass equal to the mass of the bananas hangs from the other end of the rope. The monkey and the bananas are initially balanced and at rest. Now the monkey starts to climb up the rope, moving away from the ground with speed v. What happens to the bananas?

A

They move downward at speed v

B

They remain stationary

C

They move up at speed $\frac{1}{2}v$

D

They move up at speed v

Question 218: Palette 218/454

Advance MCQ

In the given arrangement, strings and pulleys are light and all surface are frictionless. Assuming at t = 0, system is released from rest, the speed of block A at t = 2 sec is

A

$8\mathrm{ms}^{-1}$

B

$9\mathrm{ms}^{-1}$

C

$10\mathrm{ms}^{-1}$

D

None of these

Question 219: Palette 219/454

Advance MCQ

A sphere is rotating between two rough inclined walls as shown in Figure. The coefficient of friction between each wall and the sphere is $\frac{1}{3}$ . If $f_{1}$ and $f_{2}$ be the friction forces at $P$ and $Q$ . Then $\frac{f_1}{f_2}$ is

A

$\frac{4}{\sqrt{3}} + 1$

B

$\frac{1}{\sqrt{3}} + 2$

C

$\frac{1}{2} + \sqrt{3}$

D

$1 + 2\sqrt{3}$

Question 220: Palette 220/454

Advance MCQ

Three blocks $A, B$ and $C$ of equal mass $m$ are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of $A, B$ and $C$ is $\frac{1}{2}$ . The maximum value of mass of block $D$ so that the blocks $A, B$ and $C$ move without slipping over each other is

A

$6m$

B

$5m$

C

$3m$

D

$4m$

Question 221: Palette 221/454

Advance MCQ

A small particle of mass 0.36 g rests on a horizontal turntable at a distance 25 cm from the axis of spindle. The turntable is accelerated at a rate of $\frac{1}{3}$ rads $^{-2}$ . The frictional force that the table exerts on the particle 2 s after the start up is

A

40 $\mu$ N

B

30 $\mu$ N

C

50 $\mu$ N

D

60 $\mu$ N

Question 222: Palette 222/454

Advance MCQ

A block of mass m is placed at the top of a smooth wedge ABC. The wedge is rotated about an axis passing through C as shown in the figure. The minimum value of angular speed $\omega$ such that the block does not slip on the wedge is

A

$\left(\sqrt{\frac{g\sin\theta}{l}}\right)\sec\theta$

B

$\left(\sqrt{\frac{g}{l}}\right)\cos\theta$

C

$\left(\sqrt{\frac{g}{l\cos\theta}}\right)\cos\theta$

D

$\sqrt{\frac{g\sin\theta}{l}}$

Question 223: Palette 223/454

Advance MCQ

Assuming all the surfaces to be frictionless, the acceleration of block C shown in the figure is

A

$5\mathrm{ms}^{-2}$

B

$7 \, ms^{-2}$

C

$3.5 \, ms^{-2}$

D

$4 \, ms^{-2}$

Question 224: Palette 224/454

Advance MCQ

In the figure a smooth pulley of negligible weight is suspended by a spring balance. Weights of 1 kg and 5 kg are attached to the opposite ends of a string passing over the pulley and move with acceleration because of gravity. During the motion, the spring balance reads a weight of

A

6 kg

B

less than 6 kg

C

more than 6 kg

D

may be more or less than 6 kg

Question 225: Palette 225/454

Advance MCQ

A wedge of mass 2m and a cube of mass m are shown in figure. Between cube and wedge, there is no friction. The minimum coefficient of friction between wedge and ground so that wedge does not move is

A

0.10

B

0.20

C

0.25

D

0.50

Question 226: Palette 226/454

Advance MCQ

In the figure, $m_{A} = 2 \, kg$ and $m_{B} = 4 \, kg$ . The minimum value of F for which A starts slipping over B is $(g = 10 \, \text{ms}^{-2})$

A

$24\mathrm{N}$

B

$36\mathrm{N}$

C

$12\mathrm{N}$

D

$20\mathrm{N}$

Question 227: Palette 227/454

Advance MCQ

Two particles starting from a point on a circle of radius 4 m in horizontal plane move along the circle with constant speeds of $4 \, ms^{-1}$ and $6 \, ms^{-1}$ respectively in opposite directions. The particles will collide with each other after a time of

A

3 s

B

2.5 s

C

2 s

D

1.5 s

Question 228: Palette 228/454

Advance MCQ

The mass M of the hanging block in figure which will prevent the smaller block from slipping over the triangular block (assuming all the surfaces to be frictionless and the strings and the pulleys to be light) is

A

$\frac{M' + m}{\tan\theta}$

B

$(M' + m)\tan \theta$

C

$\frac{M' + m}{1 - \tan\theta}$

D

$\frac{M'+m}{\cot\theta-1}$

Question 229: Palette 229/454

Advance MCQ

In the figures, shown which of the system is at rest.

A

$A$ only

B

$A$ and $C$ only

C

A, B, and C only

D

$C$ only

Question 230: Palette 230/454

Advance MCQ

One end of the rope is fixed to vertical wall and other end is pulled by horizontal force of 20 N. The shape of flexible rope is shown in figure. The mass of rope is

A

$2\mathrm{kg}$

B

$3\mathrm{kg}$

C

$3.5\mathrm{kg}$

D

$4.5\mathrm{kg}$

Question 231: Palette 231/454

Advance MCQ

A body of mass M is kept on a rough horizontal surface (friction coefficient = $\mu$ ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F, where

A

F = Mg

B

$F = \mu Mg$

C

$Mg \leq F \leq Mg\sqrt{1 + \mu^{2}}$

D

$Mg \geq F \geq Mg\sqrt{1 - \mu^{2}}$

Question 232: Palette 232/454

Advance MCQ

For the arrangement shown in figure, the tension in the string to prevent it from sliding down is

A

$6\mathrm{N}$

B

$6.4\mathrm{N}$

C

$0.4\mathrm{N}$

D

None of these

Question 233: Palette 233/454

Advance MCQ

A chain of length $\frac{3}{2}\pi R$ and mass m is put on a mounted half cylinder as shown in figure. Chain is pulled by vertically downward force 2mg. Assuming the surface to be frictionless, acceleration of chain is

A

$2g$

B

$\frac{2g}{3}$

C

$\frac{g}{2}$

D

$\frac{5g}{3}$

Question 234: Palette 234/454

Advance MCQ

Which of the following quantities are independent of reference frame Chosen. (Consider classical mechanics only)

A

Force

B

Acceleration

C

Total energy of an isolated system

D

None of these

Question 235: Palette 235/454

Advance MCQ

The wheel has weight W. The minimum value of F required to pull the wheel up the step is

A

$W\cos \theta$

B

$W\tan \theta$

C

$W\sin \theta$

D

$W\cot \theta$

Question 236: Palette 236/454

Advance MCQ

In the arrangement shown in figure. There is a friction force between the block of masses m and 2m. Block of mass 2m is kept on a smooth horizontal plane. The mass of suspended block is m. Block A is stationary with respect to block of mass 2m. The minimum value of coefficient of friction between m and 2m is Smooth

A

$\frac{1}{2}$

B

$\frac{1}{\sqrt{2}}$

C

$\frac{1}{4}$

D

$\frac{1}{3}$

Question 237: Palette 237/454

Advance MCQ

Two blocks A and B of mass 2 kg and 4 kg are placed one over the other. A horizontal force F = 2t, which varies with time is applied on the upper block. If coefficient of friction between blocks A and B is 0.5 and horizontal surface is smooth. Then assuming t is in seconds, the total time upto which both blocks will move together without slipping over each other is

A

5 sec

B

7.5 sec

C

10 sec

D

12.5 sec

Question 238: Palette 238/454

Advance MCQ

A smooth ring of mass $M$ is threaded on a string as shown in the figure. Various portions of strings are vertical. If the ring alone is to remain at rest, then

A

$\frac{4}{M}=\frac{1}{m}+\frac{1}{m'}$

B

$\frac{2}{M} = \frac{1}{m} +\frac{1}{m^{\prime}}$

C

$\frac{1}{M}=\frac{1}{m}+\frac{1}{m'}$

D

$\frac{3}{M}=\frac{1}{m}+\frac{1}{m'}$

Question 239: Palette 239/454

Advance MCQ

Two monkeys of masses 5 kg and 4 kg are moving along a vertical rope, the former climbing up with an acceleration of $2 \, ms^{-2}$ while the later coming down with a uniform velocity of $2 \, ms^{-1}$ . Tension in the rope at the fixed support is

A

$80\mathrm{N}$

B

$100\mathrm{N}$

C

$98\mathrm{N}$

D

$108\mathrm{N}$

Question 240: Palette 240/454

Advance MCQ

Two blocks of masses $m_{1}$ and $m_{2}$ are placed in contact with each other on a horizontal platform. The coefficient of friction between the platform and the two blocks is the same. The platform moves with an acceleration. The force of interaction between the blocks is

A

zero in all cases

B

zero only if $m_{1}=m_{2}$

C

nonzero only if $m_{1} > m_{2}$

D

nonzero only if $m_{1} < m_{2}$

Question 241: Palette 241/454

Advance MCQ

A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation is $x^{2}=ay$ . If the coefficient of friction is $\mu$ , the highest distance above the x-axis at which the particle will be in equilibrium is

A

$\mu a$

B

$\mu^{2}a$

C

$\frac{1}{4}\mu^{2}a$

D

$\frac{1}{2}\mu a$

Question 242: Palette 242/454

Advance MCQ

In the figure, the wedge is accelerated to the left with an acceleration of $10\sqrt{3} \mathrm{~ms}^{-2}$ . It is seen that the block starts climbing upon the smooth inclined face of wedge. The time taken by the block to reach the top if length of the incline is $1.25 \mathrm{~m}$ is

A

$2\mathrm{s}$

B

$1\mathrm{s}$

C

$\frac{1}{\sqrt{2}}$ s

D

$\frac{1}{2}$ s

Question 243: Palette 243/454

Advance MCQ

A body is thrown up in a lift with a velocity $5 \, ms^{-1}$ relative to the lift and the time of flight is found to be 0.8 sec. The acceleration with which the lift is moving up will be $(g = 10 \, \text{ms}^{-2})$

A

$1.5 \, ms^{-2}$

B

$2 \, ms^{-2}$

C

$2.5 \, ms^{-2}$

D

$3 \, ms^{-2}$

Question 244: Palette 244/454

Advance MCQ

A person of 50 kg stands on a 25 kg platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the figure. The platform moves upwards at a constant velocity if the force with which the person pulls the rope is

A

$500\mathrm{N}$

B

$250\mathrm{N}$

C

$25\mathrm{N}$

D

$50\mathrm{N}$

Question 245: Palette 245/454

Advance MCQ

Three identical blocks are suspended on two identical springs one below the other as shown in figure. If thread is cut that supports block 1, then initially (choose one alternative only)

A

the second block falls with zero acceleration

B

the first block falls with maximum acceleration

C

both A) and B) are wrong

D

both A) and B) are correct

Question 246: Palette 246/454

Advance MCQ

A particle of mass m is released from point A on smooth fixed circular track as shown. If the particle is released from rest at t=0, then variation of normal reaction N with $(\theta)$ angular displacement from initial position is

A

B

C

D

Question 247: Palette 247/454

Advance MCQ

A $L$ shaped rod whose one rod is horizontal and other is vertical is rotating about a vertical axis as shown with angular speed $\omega$ . The sleeve shown in figure has mass $m$ and friction coefficient between rod and sleeve is $\mu$ . The minimum angular speed $\omega$ for which sleeve cannot sleep on rod is

A

$\omega=\sqrt{\frac{g}{\mu l}}$

B

$\omega=\sqrt{\frac{\mu g}{l}}$

C

$\omega=\sqrt{\frac{l}{\mu g}}$

D

None of these

Question 248: Palette 248/454

Advance MCQ

A bullet moving with a velocity of $100 \, ms^{-1}$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet, when the velocity is doubled, will be

A

4

B

6

C

8

D

10

Question 249: Palette 249/454

Advance MCQ

In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to $n$ th mass is

A

$\frac{mMg}{nm+M}$

B

$\frac{mMg}{nmM}$

C

mg

D

mng

Question 250: Palette 250/454

Advance MCQ

A ball of mass 400 g is dropped from a height of 5 m. A boy on the ground hits the ball vertically upwards with a bat with an average force of 100 N so that it attains a vertical height of 20 m. The time for which the ball remains in contact with the bat is $\left(g=10\ \mathrm{ms}^{-2}\right)$

A

0.12 sec

B

0.08 sec

C

0.04 sec

D

12 sec

Question 251: Palette 251/454

Advance MCQ

A uniform chain of length $L$ has one of its ends attached to the wall at point $A$ , while $\frac{3L}{4}$ of the length of chain is lying on table as shown in figure. The minimum coefficient of friction between table and chain, so that chain remains in equilibrium is

A

$\frac{1}{3}$

B

$\frac{1}{4}$

C

$\frac{3}{4}$

D

$\frac{1}{5}$

Question 252: Palette 252/454

Advance MCQ

A block is resting on a horizontal plate in the XY plane and co-efficient of friction between block and the plate is $\mu$ . The plate begins to move with velocity $v = bt^{2}$ in X-direction. At what time will the block starts sliding from plate

A

$\frac{\mu b}{g}$

B

$\frac{\mu bg}{2}$

C

$\frac{\mu g}{b}$

D

$\frac{\mu g}{2b}$

Question 253: Palette 253/454

Advance MCQ

80 railway wagons all of same mass $5 \times 10^{3} \mathrm{~kg}$ are pulled by an engine with a force of $4 \times 10^{5} \mathrm{~N}$ . The tension in the coupling between $30^{\text{th}}$ and $31^{\text{st}}$ wagon from the engine is

A

$25 \times 10^{4} \mathrm{~N}$

B

$20 \times 10^{4} \mathrm{~N}$

C

$32 \times 10^{4} \mathrm{~N}$

D

$40 \times 10^{4} \mathrm{~N}$

Question 254: Palette 254/454

Advance MCQ

A rod of length $L$ and mass $M$ is acted on by two unequal forces $F_{1}$ and $F_{2} (< F_{1})$ as shown in the following figure. The tension in the rod at a distance $y$ from the end $A$ is given by

A

$F_{1}\left(1 - \frac{y}{L}\right) + F_{2}\left(\frac{y}{L}\right)$

B

$F_{2}\left(1 - \frac{y}{L}\right) + F_{1}\left(\frac{y}{L}\right)$

C

$(F_{1} - F_{2})\frac{y}{L}$

D

$(F_{1} - F_{2})\frac{y}{2L}$

Question 255: Palette 255/454

Advance MCQ

A disk of mass 10 g is kept floating horizontally in the air by firing bullets each of mass 5 g with the same velocity. If 10 bullets are fired per second and the bullets rebound with the same speed, then the velocity of each bullet is

A

$196 \, cm s^{-1}$

B

$98 \, cm s^{-1}$

C

$49 \, cm s^{-1}$

D

None of these

Question 256: Palette 256/454

Advance MCQ

A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is

A

$20\mathrm{ms}^{-1}$

B

$10\mathrm{ms}^{-1}$

C

$75\mathrm{ms}^{-1}$

D

$50\mathrm{ms}^{-1}$

Question 257: Palette 257/454

Advance MCQ

A body is moving down a long inclined plane of slope $37^{\circ}$ . The coefficient of friction between the body and plane varies as $\mu = 0.3x$ , where x is the distance travelled down the plane. The body will have maximum speed at (Given that $\sin(37^{\circ}) = \frac{3}{5}$ and $g = 10 \, ms^{-2}$ )

A

x = 1.16 m

B

x = 2 m

C

the bottom of plane

D

x = 2.5 m

Question 258: Palette 258/454

Advance MCQ

A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficient of static friction and sliding friction are 0.5 and 0.4 respectively. The acceleration of the body is

A

$6 \, ms^{-2}$

B

$4.9 \, ms^{-2}$

C

$3.92 \, ms^{-2}$

D

$1 \, ms^{-2}$

Question 259: Palette 259/454

Advance MCQ

$n$ -blocks of different masses are placed on the frictionless inclined plane in contact. They are released at the same time. The force of interaction between $(n - 1)$ th and $n$ th block is

A

$(m_{n - 1} - m_n)g\sin \theta$

B

zero

C

$mng\cos \theta$

D

None of these

Question 260: Palette 260/454

Advance MCQ

A rocket of mass 120 kg is fired in the gravity free space. It ejects gases with velocity $600 \, ms^{-1}$ at the rate of $1 \, kgs^{-1}$ . What will be the initial acceleration of the rocket?

A

$1 \, ms^{-2}$

B

$5 \, ms^{-2}$

C

$10 \, ms^{-2}$

D

$15 \, ms^{-2}$

Question 261: Palette 261/454

Advance MCQ

In order to raise a mass of 100 kg, a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $\frac{5g}{4}$ relative to the rope. The tension in the rope is $(g = 10 \, \text{ms}^{-2})$

A

1432 N

B

928 N

C

1218 N

D

642 N

Question 262: Palette 262/454

Advance MCQ

A U-shaped smooth wire has a semicircular bending between A and B as shown in the figure. A bead of mass m moving with uniform speed v through the wire enters the semicircular bend at A and leaves at B. The average force, exerted by the bead on the part AB of the wire is

A

0

B

$\frac{4mv^2}{\pi d}$

C

$\frac{2mv^2}{\pi d}$

D

None of these

Question 263: Palette 263/454

Advance MCQ

A suitcase is gently dropped on a conveyor belt moving at $3 \, ms^{-1}$ . If the coefficient of friction between the belt and the suitcase is 0.5, find the displacement of the suitcase relative to conveyor belt before the slipping between the two is stopped ( $g = 10 \, ms^{-2}$ )

A

2.7 m

B

1.8 m

C

0.9 m

D

1.2 m

Question 264: Palette 264/454

Advance MCQ

A gramophone record is revolving with an angular velocity $\omega$ . A coin is placed at a distance R from the centre of the record. The static coefficient of friction is $\mu$ . The coin will revolve with the record if

A

$R > \frac{\mu g}{\omega^2}$

B

$R = \frac{\mu g}{\omega^2}$ only

C

$R < \frac{\mu g}{\omega^2}$

D

$R \leq \frac{\mu g}{\omega^2}$

Question 265: Palette 265/454

Advance MCQ

A plank is held at an angle $\alpha$ to the horizontal (figure) on two fixed supports $A$ and $B$ . The plank can slide against the supports (without friction) because of its weight $Mg$ . Acceleration and direction in which a man of mass $m$ should move so that the plank does not move

A

$g\sin \alpha \left[1 + \frac{m}{M}\right]$ down the incline

B

$g\sin \alpha \left[1 + \frac{M}{m}\right]$ down the incline

C

$g\sin \alpha \left[1 + \frac{m}{M}\right]$ up the incline

D

$g\sin \alpha \left[1 + \frac{M}{m}\right]$ up the incline

Question 266: Palette 266/454

Advance MCQ

Given that $m_{A}=20\ kg$ , $m_{B}=10\ kg$ , $m_{C}=20\ kg$ , the coefficient of friction between B and C is $\mu_{2}=0.3$ and that between C and ground $\mu_{3}=0.1$ . The least horizontal force F to start the motion of any part of the system of three blocks resting upon one another as shown in figure is $(g=10\ ms^{-2})$

A

$60\mathrm{N}$

B

$90\mathrm{N}$

C

$80\mathrm{N}$

D

$50\mathrm{N}$

Question 267: Palette 267/454

Advance MCQ

Two blocks A and B each of mass m are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on the 2 blocks A and B respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is

A

$F$

B

$\frac{F}{2}$

C

$\frac{F}{\sqrt{3}}$

D

3F

Question 268: Palette 268/454

Advance MCQ

Two trolleys 1 and 2 are moving with acceleration $a_{1}$ and $a_{2}$ respectively in the same direction. A block of mass m on trolleys 1 is in equilibrium from the frame of observer stationary w.r.t. trolleys 2. The magnitude of friction on block due to trolley is

A

$m\left(a_{1} - a_{2}\right)$

B

$ma_{2}$

C

$ma_{1}$

D

None of these

Question 269: Palette 269/454

Advance MCQ

A conveyor belt of length l is moving with velocity v. A block of mass m is pushed against the motion of conveyor belt with velocity $v_{0}$ from end B with respect to conveyor belt. Co-efficient of friction between block and belt is $\mu$ . The value of $v_{0}$ so that the amount of heat liberated as a result of retardation of the block by conveyor belt is maximum is

A

$\sqrt{\mu gl}$

B

$\sqrt{2\mu gl}$

C

$2\sqrt{\mu gl}$

D

$\sqrt{3\mu gl}$

Question 270: Palette 270/454

Advance MCQ

Assuming that the is block always remains horizontal, hence the acceleration of $B$ is

A

$6\mathrm{ms}^{-2}$

B

$2\mathrm{ms}^{-2}$

C

$4 \, ms^{-2}$

D

None of these

Question 271: Palette 271/454

Advance MCQ

All pulley shown in figure are light and there is no friction between pulley and string. Acceleration of pulley $P$ in figure is given by

A

g upward

B

g downward

C

zero

D

None of these

Question 272: Palette 272/454

Advance MCQ

The system shown in figure is released from rest. After blocks have moved through a distance $\frac{H}{3}$ , collar B stops and blocks A and C continue to move. The speed of C before it hits ground is

A

$\frac{4}{3}\sqrt{gH}$

B

$2\sqrt{\frac{gH}{3}}$

C

$\frac{\sqrt{13gH}}{3}$

D

$2\sqrt{2gH}$

Question 273: Palette 273/454

Advance MCQ

A block $A$ is made to move over an inclined plane of inclination $\theta$ with constant acceleration $a_0$ as shown in figure. Initially bob $B$ hanging from block $A$ is held vertical. Magnitude of acceleration of block $A$ relative to bob immediately after bob is released is

A

$a _ {0}$

B

$a_{0}\sin\theta$

C

$a_{0}\cos\theta$

D

$(a_{0}-g\sin\theta)$

Question 274: Palette 274/454

Advance MCQ

The massless string connecting slider A and mass B passes over two small massless smooth pulley, one which is attached to A. The end of strings are attached to mass B and roof as shown. Mass B has constant velocity $V_{0}$ directed downwards. At the instant when $Y_{A}=b$ , the magnitude of acceleration of A is

A

$\frac{V_0^2}{b}$

B

$\frac{V_0^2}{2b}$

C

$\frac{V_0^2}{4b}$

D

None of these

Question 275: Palette 275/454

Advance MSQ

When a bicycle is in motion, the force of friction exerted by the ground on the two wheels (front and rear) is $F_{1}$ and $F_{2}$ respectively. Then,

A

$F_{1}$ is in backward direction and $F_{2}$ is in the forward direction.

B

$F_{1}$ is in the forward direction and $F_{2}$ is in the backward direction.

C

both $F_{1}$ and $F_{2}$ are in forward direction.

D

both $F_{1}$ and $F_{2}$ are in backward direction.

Question 276: Palette 276/454

Advance MSQ

A reference frame attached to the earth

A

is an inertial frame by definition.

B

cannot be an inertial frame because of revolution of earth round the sun.

C

is an inertial frame because Newton's laws are applicable in this frame.

D

cannot be an inertial frame because of rotation of earth about its own axis.

Question 277: Palette 277/454

Advance MSQ

A small mirror of area A and mass m is suspended in a vertical plane by a light string. A beam of light of intensity I falls normally on the mirror and the string is deflected from the vertical by an angle $\theta$ . Assuming the mirror to be perfectly reflecting have

A

radiation pressure equal to $\frac{2I}{c}$

B

radiation pressure equal to $\frac{I}{2c}$

C

$\tan\theta=\frac{2IA}{mgc}$

D

$\tan\theta=\frac{IA}{2mgc}$

Question 278: Palette 278/454

Advance MSQ

Two blocks A and B of the same mass are joined by a light inextensible string and placed on a horizontal surface. An external horizontal force P acts on A. The tension in the string is T. The forces of friction acting on A and B are $f_{1}$ and $f_{2}$ respectively. The limiting value of $f_{1}$ and $f_{2}$ is $f_{0}$ . When P is gradually increased, then

A

for $P < f_0$ , $T = 0$

B

for $f_{0} < P < 2f_{0}$ , $T=P-f_{0}$

C

for $P > 2f_{0}$ , $T = \frac{P}{2}$

D

None of the above

Question 279: Palette 279/454

Advance MCQ

The maximum value of the force F such that the block shown in the arrangement, does not move is

A

$20\mathrm{N}$

B

$10\mathrm{N}$

C

$12\mathrm{N}$

D

$15\mathrm{N}$

Question 280: Palette 280/454

Advance MSQ

Two blocks A and B of mass 10 kg and 20 kg, respectively are placed as shown in figure. Coefficient of friction between all the surfaces is $0.2 \left( g = 10 \, \text{ms}^{-2} \right)$ . Then

A

tension in the string is 306 N

B

tension in the string is 132 N

C

force exerted by the wall on B is 265 N

D

acceleration of block B is $4.7 \, ms^{-2}$

Question 281: Palette 281/454

Advance MSQ

Two cubes of masses $m_{1}$ and $m_{2}$ lie on frictionless slopes of a block A which rests on a horizontal table. The cubes are connected by a string which passes over a pulley as shown in figure. If $a_{0}$ be the horizontal acceleration to which the whole system (block + masses) is subjected so that $m_{1}$ and $m_{2}$ do not move and T be the tension in the string in that situation then find $a_{0}$ and T

A

$a _ {0} = \left(\frac {m _ {1} \sin \alpha + m _ {2} \sin \beta}{m _ {1} + m _ {2}}\right) g$

B

$a_{0}=\left(\frac{m_{1}\sin\alpha+m_{2}\sin\beta}{m_{1}\cos\alpha+m_{2}\cos\beta}\right)g$

C

$T = \frac{m_{1} m_{2}}{m_{1} + m_{2}} g \sin (\alpha + \beta)$

D

$T = \left( \frac{m_{1} m_{2}}{m_{1} \cos \alpha + m_{2} \cos \beta} \right) g \sin (\alpha - \beta)$

Question 282: Palette 282/454

Advance MSQ

A block of mass 1 kg is stationary with respect to a conveyor belt that is accelerating with $1 \, ms^{-2}$ upwards at an angle of $30^{\circ}$ as shown in figure. Which of the following statement(s) is/are correct. ( $g = 10 \, ms^{-2}$ )

A

force of friction on the block is 1 N upwards

B

force of friction on the block is 6 N upwards

C

contact force between the block and the belt is 10.5 N

D

contact force between the block and the belt is $5\sqrt{3}$ N

Question 283: Palette 283/454

Advance MSQ

A body is kept on a smooth inclined plane having an inclination of 1 in x. Then,

A

slope of inclined plane is $\frac{1}{x}$ .

B

slope of inclined plane is $\frac{1}{\sqrt{x^2 - 1}}$ .

C

for the body of mass $m$ to remain stationary relative to the incline, the incline must offer a normal reaction of $mg\frac{x}{\sqrt{x^2 - 1}}$ .

D

for the body to remain stationary relative to the incline, the incline must be given a horizontal acceleration of $\frac{g}{\sqrt{x^{2}-1}}$ .

Question 284: Palette 284/454

Advance MSQ

Two blocks A and B of equal mass m are connected through a light inextensible string and arranged as shown in figure. Friction is absent everywhere. When the system is released from rest

A

tension in string is $\frac{mg}{2}$ .

B

tension in string is $\frac{mg}{4}$ .

C

acceleration of $A$ is $\frac{g}{2}$ .

D

acceleration of $A$ is $\frac{3}{4} g$ .

Question 285: Palette 285/454

Advance MSQ

A block of weight W is suspended from a spring balance. The lower surface of the block rests on a weighing machine. The spring balance reads $W_{1}$ and the weighing machine reads $W_{2}$ . Assuming all W, $W_{1}$ , $W_{2}$ to have the same units, which of the following is/are correct?

A

$W = W_{1} + W_{2}$ , when the system is at rest.

B

$W > W_{1} + W_{2}$ , when the system moves down with some acceleration.

C

$W_{1} > W_{2}$ , when the system moves up with some acceleration.

D

Data is insufficient to find the relation between $W_{1}$ and $W_{2}$ .

Question 286: Palette 286/454

Advance MSQ

A uniform chain of length L lies on a smooth horizontal table with its length perpendicular to the edge of the table and a small portion of the chain is hanging over the edge. The chain starts sliding due to the weight of the hanging part.

A

The acceleration of the chain is $\frac{gx}{L}$ ; where $x$ is the length of the hanging part of chain.

B

The acceleration of the chain is $\frac{g}{L}(L-x)$ ; where x is the length of the hanging part of chain.

C

The velocity of the chain is $x\sqrt{\frac{g}{L}}$ , where x is the length of the hanging part of chain.

D

The velocity of the chain is $(L-x)\sqrt{\frac{g}{L}}$ ; where x is the length of the hanging part of chain.

Question 287: Palette 287/454

Advance MSQ

An amusement park ride called "The Spinning Terror" is a large vertical drum which spins so fast that everyone inside stays pinned against the wall when the floor drops away

A

The minimum angular velocity is $\omega_{\min} = \sqrt{\frac{g}{\mu R}}$ for everyone to stay inside.

B

The minimum linear velocity is $v_{\min} = \sqrt{\frac{g}{\mu R}}$ for everyone to stay inside.

C

The minimum angular velocity is $\omega_{\min} = \sqrt{\frac{gR}{\mu}}$ for everyone to stay inside.

D

The minimum linear velocity is $v_{\min} = \sqrt{\frac{gR}{\mu}}$ for everyone to stay inside.

Question 288: Palette 288/454

Advance MSQ

In the arrangement shown $W_{1} = 200 \, N$ , $W_{2} = 100 \, N$ , $\mu = 0.25$ for all surfaces in contact. The block $W_{1}$ just slides under the block $W_{2}$ .

A

A pull of 50 N is to be applied on $W_{1}$ .

B

A pull of 90 N is to be applied on $W_{1}$ .

C

Tension in the string AB is $10\sqrt{2}$ N.

D

Tension in the string $AB$ is $20\sqrt{2}\mathrm{N}$ .

Question 289: Palette 289/454

Advance MSQ

A weight $W$ can be just supported on a rough inclined plane by a force $P$ either acting along the plane or horizontally. The angle of friction is $\phi$ and $\theta$ is the angle which incline makes with the horizontal.

A

The incline makes an angle with the horizontal twice the angle of friction i.e., $\theta = 2\phi$ .

B

The incline make an angle with the horizontal equal to the angle of friction i.e., $\theta = \phi$ .

C

The ratio of the force to the weight is $\frac{P}{W} = \cot \phi$ .

D

The ratio of the force to the weight is $\frac{P}{W} = \tan \phi$

Question 290: Palette 290/454

Advance MCQ

An insect crawls up a hemispherical surface very slowly as shown in figure. The coefficient of friction between the surface and the insect is $\frac{1}{3}$ . If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by

A

$\cot \alpha = 3$

B

$\tan \alpha = 3$

C

$\sec \alpha = 3$

D

$\operatorname{cosec} \alpha = 3$

Question 291: Palette 291/454

Advance MCQ

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by

A

$\sqrt{2} Mg$

B

$\sqrt{2} mg$

C

$\sqrt{(M + m)^2 + m^2} g$

D

$\sqrt{(M + m)^2 + M^2} g$

Question 292: Palette 292/454

Advance MSQ

A boy of mass m kg slides down a light rope attached to a fixed spring balance, with an acceleration a. The reading of the spring balance is M kg.

A

The tension in the rope is $T = Mg N$

B

$m = M \left( 1 + \frac{a}{g} \right)$

C

$m=\frac{Mg}{g-a}$

D

The force of friction exerted by the rope on the boy is $f = m(g - a)$ N

Question 293: Palette 293/454

Advance MSQ

A block of weight 9.8 N is placed on a table. The table surface exerts an upward force of 10 N on the block. Assume $g = 9.8 \, ms^{-2}$ .

A

The block exerts a force of 19.8 N on the table.

B

The block exerts a force of 10 N on the table.

C

The block has an upward acceleration.

D

The block exerts a force of 9.8 N on the table.

Question 294: Palette 294/454

Advance MCQ

A solid uniform cube of mass m is pressed against a rough vertical wall by applying a force F as shown in the figure. The cube is stationary. Choose the incorrect option

A

normal force by the wall on the cube is F

B

friction force on the cube is mg

C

the torque of force F about the centre of mass of the cube is zero

D

the torque of normal force about the centre of mass of the cube is zero

Question 295: Palette 295/454

Advance MSQ

Two blocks A and B of mass 4 kg and 2 kg respectively connected by a spring of force constant $k = 100 \, Nm^{-1}$ are placed on an inclined plane of inclination $30^{\circ}$ as shown in figure. If the system is released from rest, which one of the following statement(s) is/are correct ( $g = 10 \, ms^{-2}$ )

A

there will be no compression/elongation in the spring if all surfaces are smooth

B

maximum compression of the spring is 10 cm if all surfaces are smooth

C

maximum elongation in the spring is 60 cm if all the surfaces are smooth

D

there will be elongation in the spring if $A$ is smooth and $B$ is rough

Question 296: Palette 296/454

Advance MSQ

Newton's laws are valid in

A

any reference frame.

B

a reference frame moving with constant velocity with respect to an inertial frame.

C

all reference frames which are at rest with respect to an inertial frame.

D

the reference frame attached to the earth.

Question 297: Palette 297/454

Advance MSQ

A light vertical chain is used to haul up an object of mass $M$ attached to its lower end. The vertical pull applied has a magnitude $F$ at $t = 0$ and it decreases at a uniform rate of $f\mathrm{Nm}^{-1}$ over a distance $s$ through which the object is raised.

A

The acceleration of the object is $\left(\frac{F - fy - Mg}{M}\right)$ when the object is raised through a distance $y(< s)$ .

B

The acceleration of the object is constant.

C

The object has a velocity $\sqrt{\frac{2s}{M}\left(F - Mg - \frac{fs}{2}\right)}$ when it has been raised through a distance $s$ .

D

The object has a velocity $\sqrt{\frac{s}{g}}$ when it has been raised through a distance $s$ .

Question 298: Palette 298/454

Advance MSQ

A lift is moving downwards. A body of mass $m$ kept on the floor of the lift is pulled horizontally. If $\mu$ is the coefficient of friction between the surfaces in contact then,

A

frictional resistance offered by the floor is $\mu mg$ when lift moves up with a uniform velocity of $5 \, ms^{-1}$ .

B

frictional resistance offered by the floor is $\mu mg$ when lift moves up with a uniform velocity of $3\ ms^{-1}$ .

C

frictional resistance offered by the floor is $5 \, m\mu$ when lift accelerates down with an acceleration of $4.8 \, ms^{-2}$ .

D

frictional resistance $(f)$ offered by the floor must lie in the range $0 \leq f < \infty$ .

Question 299: Palette 299/454

Advance MSQ

The two blocks A and B of equal mass are initially in contact when released from rest on the inclined plane. The coefficients of friction between the inclined plane and A and B are $\mu_{1}$ and $\mu_{2}$ respectively.

A

If $\mu_{1} > \mu_{2}$ , the blocks will always remain in contact.

B

If $\mu_{1} < \mu_{2}$ , the blocks will slide down with different accelerations.

C

If $\mu_{1} > \mu_{2}$ , the blocks will have a common acceleration $\frac{1}{2} (\mu_1 + \mu_2)g\sin \theta$ .

D

If $\mu_{1} < \mu_{2}$ , the blocks will have a common acceleration $\frac{\mu_{1}\mu_{2}g}{\mu_{1} + \mu_{2}}\sin \theta$ .

Question 300: Palette 300/454

Advance MCQ

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 301: Palette 301/454

Advance MSQ

A simple pendulum with a bob of mass m is suspended from the roof of a car moving with a horizontal acceleration a.

A

The string makes an angle of $\tan^{-1}\left(\frac{g}{a}\right)$ with the vertical.

B

The string makes an angle of $\tan^{-1}\left(\frac{a}{g}\right)$ with the vertical.

C

The tension in the string is $m\sqrt{g^2 - a^2}$ .

D

The tension in the string is $m\sqrt{a^{2}+g^{2}}$ .

Question 302: Palette 302/454

Advance MSQ

In the arrangement shown in figure pulley is smooth and massless and string is light. Friction coefficient between $A$ and $B$ is $\mu$ . Friction is absent between $A$ and plane. Select the correct alternative(s)

A

acceleration of the system is zero if $\mu \geq \left(\frac{m_B - m_A}{2m_B}\right)\tan \theta$ and $m_B > m_A$

B

force of friction between $A$ and $B$ is zero if $m_A = m_B$

C

B moves upwards if $m_{B} < m_{A}$

D

tension in the string is $mg \sin \theta$ if $m_{A} = m_{B} = m$

Question 303: Palette 303/454

Advance MSQ

A block A of mass 500 g is placed on a smooth horizontal table with a light string attached to it. The string passes over a smooth pulley P at the end of the table (as shown) and is connected to other block B of mass 200 g. Initially the block A is at a distance of 200 cm from the pulley and is moving with a speed of $50 \, cms^{-1}$ to the left. At t = 1 s

A

the block is at a distance of 90 cm from the pulley P.

B

the block is at a distance of 110 cm from the pulley P.

C

the block has a velocity of $230 \, cms^{-1}$ towards left.

D

the block has a velocity of $230 \, cm s^{-1}$ towards right.

Question 304: Palette 304/454

Advance MSQ

Two masses m and $M(m < M)$ are joined by a light string passing over a smooth and light pulley (as shown).

A

The acceleration of each mass is $\left(\frac{M - m}{M + m}\right)g$ .

B

The tension in the string connecting masses is $\left(\frac{2Mm}{M + m}\right)g$ .

C

The thrust acting on the pulley is $\left(\frac{4Mm}{M + m}\right)g$ .

D

The centre of mass of the system (i.e. $M$ and $m$ ) moves down with an acceleration of $\left(\frac{M - m}{M + m}\right)^2 g$ .

Question 305: Palette 305/454

Advance MSQ

In the arrangement shown in figure all surfaces are smooth. Select the correct alternative(s)

A

contact force between the two blocks is zero if $\frac{m_A}{m_B} = \tan \theta$

B

for any value of $\theta$ acceleration of $A$ and $B$ are equal

C

normal reactions exerted by the wedge on the blocks are equal

D

contact force between the two is zero for any value of $m_{A}$ or $m_{B}$

Question 306: Palette 306/454

Advance MSQ

A cricket ball of mass 150 g is moving with a velocity of $12 \, ms^{-1}$ and is hit by a bat so that it turns back with a velocity of $20 \, ms^{-1}$ . The force of blow acts for a time of 0.01 s. Then,

A

the change in momentum of ball is $4.8 \, kgms^{-1}$ .

B

the average force exerted by the bat on the ball is 480 N.

C

change in momentum of the ball is $1.2 \, kgms^{-1}$

D

the average force exerted by the bat on the ball is 120 N.

Question 307: Palette 307/454

Advance MSQ

In the pulley system shown the movable pulleys A, B and C have mass m each, D and E are fixed pulleys. The strings are vertical, light and inextensible. Then,

A

the tension throughout the string is the same and equals $T=\frac{2mg}{3}$ .

B

pulleys A and B have acceleration $\frac{g}{3}$ each in downward direction and pulley C has acceleration $\frac{g}{3}$ in upward direction.

C

pulleys A, B and C all have acceleration $\frac{g}{3}$ in downward direction.

D

pulley A has acceleration $\frac{g}{3}$ in downward direction and pulleys B and C have acceleration $\frac{g}{3}$ each in upward direction.

Question 308: Palette 308/454

Advance MSQ

Two masses of 10 kg and 20 kg are connected by a light spring as shown. A force of 200 N acts on a 20 kg mass as shown. At a certain instant the acceleration of 10 kg mass is $12 \, ms^{-2}$ .

A

At that instant the 20 kg mass has an acceleration of $12 \, ms^{-2}$ .

B

At that instant the 20 kg mass has an acceleration of $4 \, ms^{-2}$ .

C

The stretching force in the spring is 120 N.

D

The collective system moves with a common acceleration of $30 \, ms^{-2}$ when the extension in the connecting spring is the maximum.

Question 309: Palette 309/454

Advance MSQ

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

A

its velocity is constant.

B

its acceleration is constant.

C

its kinetic energy is constant.

D

it moves in a circular path.

Question 310: Palette 310/454

Advance MSQ

A particle of mass M is moving with acceleration $a_{0}$ as measured by an observer 1 standing in a frame of reference moving with a uniform velocity. Another observer 2 is standing in a frame of reference moving with acceleration a.

A

Observer 1 measures the force acting on the body as $Ma_{0}$ .

B

Observer 2 measures the force acting on the body as Ma.

C

Observer 2 measures the force acting on the body as $Ma_0 - Ma$ .

D

Observer 1 is standing in an inertial frame of reference and observer 2 is standing in a non-inertial frame of reference.

Question 311: Palette 311/454

Advance MSQ

Two blocks on a rough incline are connected by a light string that passes over a frictionless light pulley as shown. Assuming $m_{1} > m_{2}$ and taking the coefficient of kinetic friction for each block to be $\mu$ get acceleration of the blocks as

A

$\mathrm{(A)} \quad a = \frac {\left[ \left(m _ {1} - m _ {2}\right) \sin \theta - \mu \left(m _ {1} + m _ {2}\right) \cos \theta \right] g}{\left(m _ {1} + m _ {2}\right)} \text {for} m _ {1}$

B

$a = \frac {\left[ \mu (m _ {1} + m _ {2}) \cos \theta - (m _ {1} - m _ {2}) \sin \theta \right] g}{(m _ {1} + m _ {2})} \text { for } m _ {2} \tag {B}$

C

$a = g(\sin\theta - \mu\cos\theta)$

D

$a = g(\cos\theta - \mu\sin\theta)$

Question 312: Palette 312/454

Advance MSQ

Two masses $m_{1}$ and $m_{2}$ are connected by a light string which passes over the top of an inclined plane making an angle of $30^{\circ}$ with the horizontal such that one mass rests on the plane and other hangs vertically. It is found that $m_{1}$ hanging vertically can draw $m_{2}$ up the full length of the incline in half the time in which $m_{2}$ hanging vertically draws $m_{1}$ up the full length of the incline. Assuming the surfaces in contact to be frictionless and pulley to be light and smooth, have

A

the ratio of acceleration in the two cases respectively as 4.

B

the ratio of acceleration in the two cases respectively as $\frac{1}{4}$ .

C

the ratio of masses $m_{1}$ and $m_{2}$ as $\frac{3}{2}$ .

D

the ratio of masses $m_{1}$ and $m_{2}$ as $\frac{2}{3}$ .

Question 313: Palette 313/454

Advance MSQ

Which of the following statement(s) is (are) correct about friction?

A

The coefficient of friction between two bodies is largely independent of area of contact.

B

The frictional force can never exceed the reaction force on a body from the supporting surface.

C

Rolling friction is generally smaller than sliding friction.

D

Friction is due to irregularities of the surfaces in contact.

Question 314: Palette 314/454

Advance MSQ

Two blocks of masses 2.9 kg and 1.9 kg are suspended from a rigid support S by two inextensible wires each of length 1 m as shown in figure. The upper wire has negligible mass and lower wire has a uniform mass of $0.2 \, kgm^{-1}$ . The whole system of blocks, wires and support have an upward acceleration of $a_{0} = 0.2 \, ms^{-2}$ . Taking $g = 9.8 \, ms^{-2}$ , have

A

tension at the midpoint of upper rope is 50 N.

B

tension at the midpoint of upper rope is 40 N.

C

tension at the midpoint of lower rope is 19.6 N.

D

tension at the midpoint of lower rope is 20 N.

Question 315: Palette 315/454

Advance MSQ

The spheres A and B as shown have mass M each. The strings SA and AB are light and inextensible with tensions $T_{1}$ and $T_{2}$ respectively. A constant horizontal force F = Mg is acting on B. For the system to be in equilibrium have

A

$\tan\phi=1$

B

$\tan \theta = 0.5$

C

$T_{2}=\sqrt{2}$ Mg

D

$T_{1}=\sqrt{5}$ Mg

Question 316: Palette 316/454

Advance MSQ

A person is sitting on a moving train and is facing the engine. He tosses up a coin which falls behind him.

A

The train is moving forward and gaining speed.

B

The train is moving forward and losing speed.

C

The train is moving backward and losing speed.

D

The train is moving backward and gaining speed.

Question 317: Palette 317/454

Advance MSQ

In the diagram shown, the acceleration of the block B as shown in figure relative to the block A and relative to ground is $a_{BA}$ and $a_{BG}$ , respectively. If the block A is moving toward left with an acceleration $a_{0}$ , then

A

$a_{BA} = 2a_{0}$

B

$a_{BG} = 3a_{0}$

C

$a_{BG} = 3a_{0}$

D

$a_{BG} = a_{0}\sqrt{10 + 6\cos\theta}$

Question 318: Palette 318/454

Advance MSQ

In the adjoining figure if acceleration of $M$ with respect to ground is $a$ , then

A

acceleration of $m$ with respect to $M$ is $a$ .

B

acceleration of $m$ with respect to ground is $2a\sin \left(\frac{\alpha}{2}\right)$ .

C

acceleration of $m$ with respect to ground is $a$ .

D

acceleration of m with respect to ground is $a \tan \alpha$ .

Question 319: Palette 319/454

Advance MSQ

A particle is resting over a smooth horizontal floor. At t = 0, a horizontal force starts acting on it. Magnitude of the force increases with time as F = kt, where k is a constant. The two curves are drawn for this particle as shown.

A

Curve-1 shows acceleration versus time

B

Curve-2 shows velocity versus time

C

Curve-2 shows velocity versus acceleration

D

None of these

Question 320: Palette 320/454

Advance MSQ

A trolley of mass $m_{1}$ is to be moved such as to keep block A of mass $m_{2}$ at rest with respect to it. A bucket of mass $m_{3}$ (with water) in it is placed on trolley. Coefficient of friction between the block A and trolley is $\mu$ . The trolley is moved with acceleration so that block does not slip

A

The minimum coefficient of friction between bucket and trolley is $\frac{\mu}{2}$ .

B

The acceleration of trolley is $\frac{g}{\mu}$ .

C

The inclination of water surface in the bucket with horizontal in absence of any slipping is $\tan^{-1}\left(\frac{1}{\mu}\right)$ .

D

Force on trolley is $(m_{1}+m_{2}+m_{3})\frac{g}{\mu}$ .

Question 321: Palette 321/454

Advance MSQ

Force $F$ is applied on block $B$ and the system is at rest. All surfaces are rough. Which of the following statements is/are correct?

A

Friction force on C due to B is zero.

B

Friction on C due to ground is equal to friction force on B.

C

Friction force on A must be zero.

D

Friction force on A depends upon force applied F.

Question 322: Palette 322/454

Advance MSQ

Which of the following statements are true for a moving body?

A

if its speed changes, its velocity must change and it must have some acceleration

B

if its velocity changes, its speed must change and it must have some acceleration

C

if its velocity changes, its speed may or may not change, and it must have some acceleration

D

if its speed changes, but direction of motion does not change, its velocity may remain constant

Question 323: Palette 323/454

Advance MSQ

Speed of a body moving in a circular path changes with time as v = 2t, then

A

magnitude of acceleration remains constant

B

magnitude of acceleration increases

C

angle between velocity and acceleration remains constant

D

angle between velocity and acceleration increases

Question 324: Palette 324/454

Advance MSQ

Two blocks A and B of mass 1 kg each are connected by an ideal string that passes over a smooth pulley that is fixed on a smooth fixed wedge as shown. If the ratio of normal reaction on block A and on block B is $\frac{4}{3}$ then

A

$\cos\theta=\frac{4}{5}$

B

$\sin\theta=\frac{4}{5}$

C

acceleration of blocks is $\frac{g}{10}$ ms $^{-2}$

D

acceleration of blocks is $\frac{g}{5}$ ms $^{-2}$

Question 325: Palette 325/454

Advance MSQ

Two uniform identical ladders AB and AC each of mass m leans against each other and a string is tied between them which is horizontal. The system stands on a smooth horizontal surface as shown, then, string is connected from ends B and C.

A

the force exerted by one rod on other at $A$ is equal to the tension $T$ in the string

B

tension in string $T=\left(\frac{mg}{2}\right)\cot\theta$

C

tension in string $T=\left(\frac{mg}{2}\right)\tan\theta$

D

None of these

Question 326: Palette 326/454

Advance MSQ

Two blocks are pushed against a rough wall and the system is at rest as shown in figure. Select the correct statement(s).

A

Friction force on block $A$ due to $B$ is in upward direction

B

Friction force on block A due to wall is 150 N

C

Minimum force required to keep system at rest is 375 N

D

Friction of block B due to A increases with increase in force applied F

Question 327: Palette 327/454

Advance MSQ

A block of mass m is moving on a rough horizontal surface and its velocity at time t = 0 is found to be $\vec{v}$ then a time varying horizontal force F = 2t is applied on the body in the direction of its velocity then, after the application of force

A

speed of block increases

B

first decreases then increases

C

work done by friction is negative

D

work done by applied force is positive

Question 328: Palette 328/454

Advance MSQ

A body moves in a circular path of radius R with deceleration so that at any moment of time its tangential and normal accelerations are equal in magnitude. At the initial moment t = 0, the velocity of body is $v_{0}$ then the velocity of body will be

A

$v = \frac{v_0}{1 + \left(\frac{v_0t}{R}\right)}$ at time $t$ .

B

$v = v_{0} e^{-\frac{S}{R}}$ after it has moved S meter.

C

$v = v_{0} e^{-SR}$ after it has moved S meter.

D

None of these

Question 329: Palette 329/454

Advance MSQ

A body is moving with constant velocity on the path shown.

A

Normal reaction exerted on body by path is greatest at $N_{B}$ .

B

Normal reaction exerted on body by path is least at $N_{C}$ .

C

Normal force is greater than weight at B.

D

Normal force is lesser than weight at A, D.

Question 330: Palette 330/454

Advance MSQ

In the figure shown the pulley is ideal and strings are massless. If mass m of hanging block is the minimum mass to keep the system in equilibrium, then $\left(g=10\ \mathrm{ms}^{-2}\right)$

A

$m = 2.5 \, kg$

B

$m = 5 \, kg$

C

force applied by 20 kg block on inclined plane is 179 N

D

force applied by 20 kg block on inclined plane is 223 N

Question 331: Palette 331/454

Advance MSQ

The blocks $(m_{2} > m_{1})$ are held in such a manner that spring is unstretched initially. Consider the situation at the time of releasing the blocks $(t = 0)$ and short time after releasing the blocks $(t > 0)$ . Acceleration of block of mass $m_{1}$ is $a_{1}$ and $m_{2}$ is $a_{2}$ , then

A

$t = 0, a_{1} = a_{2}$

B

$t = 0, a_{1} < a_{2}$

C

t > 0, $a_{1} = a_{2}$

D

t > 0, $a_{1} < a_{2}$

Question 332: Palette 332/454

Advance MSQ

Three blocks are arranged as shown. ABCD is the horizontal plane. Strings are massless and both pulley stands vertical while the strings connecting blocks $m_{1}$ and $m_{2}$ are also vertical and perpendicular to each other. The masses $m_{1}$ and $m_{2}$ are 3 kg and 4 kg respectively. Coefficient of friction between the block $m_{3}=10$ kg and surface is $\mu=0.6$ , then select the correct statement(s).

A

The system of blocks can be in equilibrium

B

At equilibrium frictional force on block $m_{3}$ is 60 N

C

At equilibrium frictional force on block $m_{3}$ 50 N

D

Total force applied by surface on block $m_{3}$ is $50\sqrt{5}$ N

Question 333: Palette 333/454

Advance MSQ

Three large box are kept stationary over one other as shown in figure. A horizontal force 20 N acts on middle block as shown in figure. Then select the correct statement(s).

A

Acceleration of lowest block is $4.5 \, ms^{-2}$ .

B

Acceleration of upper most block is $2 \, ms^{-2}$ .

C

Friction between middle and lower block is 12 N.

D

Friction between middle and upper block is 2 N.

Question 334: Palette 334/454

Advance MSQ

A car of mass $M$ is moving horizontally on a circular path of radius $r$ . At an instant its speed is $v$ and is increasing at a rate $a$ .

A

The acceleration of the car is towards the centre of the path

B

The magnitude of the frictional force on the car is greater than $\frac{mv^{2}}{r}$

C

The friction coefficient between the ground and the car is not less than $\frac{a}{g}$

D

The friction coefficient between the ground and the car is $\mu = \tan^{-1}\left(\frac{v^2}{rg}\right)$

Question 335: Palette 335/454

Advance MSQ

A person applies a constant force $\vec{F}$ on a particle of mass m and finds that the particle moves in a circle of radius r with a uniform speed v as seen (in the plane of motion) from an inertial frame of reference.

A

This is not possible

B

There are other forces on the particle

C

The resultant of the other forces is $\frac{mv^{2}}{r}$ towards the centre

D

The resultant of the other forces varies in magnitude as well as in direction

Question 336: Palette 336/454

Advance MSQ

A body of mass 5 kg is suspended by the strings making angles $60^{\circ}$ and $30^{\circ}$ with the horizontal as shown in figure $(g = 10 \, \text{ms}^{-2})$ .

A

$T_{1}=25\ N$

B

$T_{2}=25\ N$

C

$T_{1}=25\sqrt{3}$ N

D

$T_{2}=25\sqrt{3}$ N

Question 337: Palette 337/454

Advance MSQ

In the figure shown, a small block of mass m is kept on M, placed on a horizontal surface. All surfaces are smooth and a force F is applied on M.

A

The acceleration of m w.r.t. ground is $\frac{F}{m}$

B

The acceleration of m w.r.t. ground is zero

C

The time taken by $m$ to separate from $M$ is $\sqrt{\frac{2lm}{F}}$

D

The time taken by $m$ to separate from $M$ is $\sqrt{\frac{2lM}{F}}$

Question 338: Palette 338/454

Advance MSQ

A 20 kg block is placed on top of 50 kg block as shown in figure. A horizontal force F acting on A produces an acceleration of $3 \, ms^{-2}$ in A and $2 \, ms^{-2}$ in B as shown in figure. For this situation mark out the correct statement(s).

A

The friction force between A and B is 40 N.

B

The net force acting on A is 150 N.

C

The value of F is 190 N.

D

The value of F is 150 N.

Question 339: Palette 339/454

Advance MCQ

A wedge of mass $m_{1}$ and a block of mass $m_{2}$ are in equilibrium as shown. Inclined surface of the wedge has an inclination $\alpha$ with the horizontal. Each surface is frictionless. The normal reaction on the wedge may be

A

$m_{2}g\cos\alpha$

B

$m_{2}g\sin\alpha\cos\alpha$

C

$m_{1}g + m_{2}g\cos^{2}\alpha$

D

$m_{1}g + m_{2}g \sin \alpha \cos \alpha$

Question 340: Palette 340/454

Advance MCQ

Statement-1: Rate of change of linear momentum is equal to external force. Statement-2: There is equal and opposite reaction to every action.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 341: Palette 341/454

Advance MCQ

Statement-1: A block of mass m is kept at rest on an inclined plane, the rest force applied by the surface to the block will be mg. Statement-2: Normal contact force is the resultant of normal contact force and friction force.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 342: Palette 342/454

Advance MCQ

Statement-1: Friction force always opposes the motion. Statement-2: Friction force can support the motion.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 343: Palette 343/454

Advance MCQ

Statement-1: A table cloth can be pulled from a table without disturbing a glass kept on it. Statement-2: Every body opposes the change in its state.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 344: Palette 344/454

Advance MCQ

Statement-1: The driver of a moving car sees a wall in front of him. To avoid collision, he should apply brakes rather than taking a turn away from the wall. Statement-2: Friction force is needed to stop the car or taking a turn on a horizontal road.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 345: Palette 345/454

Advance MCQ

Statement-1: Two teams having a tug of war always pull equally hard on one another. Statement-2: The team that pushes harder against the ground, in a tug of war, wins.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 346: Palette 346/454

Advance MCQ

Statement-1: A bird alights on a stretched wire depressing it slightly. The increase in tension of the wire is more than the weight of the bird Statement-2: The tension must be more than the weight as it is required to balance weight.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 347: Palette 347/454

Advance MCQ

Statement-1: Newton's First Law is merely a special case $(a = 0)$ of the Second Law. Statement-2: Newton's First Law defines the frame from where Newton's Second Law; $\vec{F} = m\vec{a}$ , $\vec{F}$ representing the net real force acting on a body; is applicable.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 348: Palette 348/454

Advance MCQ

Statement-1: Two smooth blocks are kept on a smooth inclined plane such that one block is kept over other when a force is applied on upper block acceleration of lower block is unaffected. Statement-2: Acceleration of a block on smooth inclined plane is $g \sin \theta$ .

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 349: Palette 349/454

Advance MCQ

Statement-1: A uniform rope of mass m hangs freely from a ceiling. A monkey of mass M climbs up the rope with an acceleration a. The force exerted by the rope on the ceiling is $M(a + g) + mg$ . Statement-2: Action and reaction force are acting on two different bodies

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 350: Palette 350/454

Advance MCQ

Statement-1: According to Newton's Second Law of motion action and reaction forces are equal and opposite Statement-2: Action and reaction forces never cancel out each other because they are acting on different objects.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 351: Palette 351/454

Advance MCQ

Statement-1: Two balls are projected with different velocities at angles $30^{\circ}$ and $45^{\circ}$ . Horizontal range must be maximum for the ball which is projected at $45^{\circ}$ . Statement-2: For a given velocity $R = \frac{u^{2} \sin 2\theta}{g}$ .

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 352: Palette 352/454

Advance MCQ

Statement-1: A block of mass m is placed on a smooth inclined plane of inclination $\theta$ with the horizontal. The force exerted by the plane on the block has a magnitude mg cos $\theta$ . Statement-2: Normal reaction always acts perpendicular to the contact surface.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 353: Palette 353/454

Advance MCQ

Statement-1: A particle is found to be at rest when seen from a frame $S_{1}$ and moving with a constant velocity when seen from another frame $S_{2}$ . can say both the frames are inertial. Statement-2: All frames moving uniformly with respect to an inertial frame are themselves inertial.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 354: Palette 354/454

Advance MCQ

Statement-1: Coefficient of friction can be greater than unity. Statement-2: Force of friction is dependent on normal reaction and ratio of force of friction and normal reaction cannot exceed unity.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 355: Palette 355/454

Advance MCQ

Statement-1: In high jump, it hurts less when an athlete lands on a heap of sand. Statement-2: Because of greater distance and hence greater time over which the motion of an athlete is stopped, the athlete experience less force when lands on heap of sand.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 356: Palette 356/454

Advance MCQ

Statement-1: For a boy it is difficult to run at high speed on a rainy day. Statement-2: Coefficient of friction $\mu$ is decreased due to rain.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 357: Palette 357/454

Advance MCQ

Statement-1: A body in equilibrium has to be at rest only. Statement-2: A body in equilibrium may be moving with a constant speed along a straight line path.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 358: Palette 358/454

Advance MCQ

Statement-1: Inertia is the property by virtue of which the body is unable to change by itself the state of rest. Statement-2: The bodies do not change their state unless acted upon by an un-balanced external force.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 359: Palette 359/454

Advance MCQ

Statement-1: Pulling (refer figure 1) is easier than pushing (refer figure 2) on a rough surface. Figure 1 Figure 2 Statement-2: Normal reaction is less in pulling than is pushing.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 360: Palette 360/454

Advance MCQ

Statement-1: A block is lying stationary as on inclined plane and coefficient of friction is $\mu$ . Friction on block is $\mu mg \cos \theta$ . Statement-2: Contact force on block is mg.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 361: Palette 361/454

Advance MCQ

Statement-1: Static frictional force is always greater than kinetic frictional force. Statement-2: (Coefficient of static friction) $\mu_{s} > \mu_{k}$ (coefficient of kinetic friction).

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 362: Palette 362/454

Advance MCQ

Statement-1: Two particles are moving towards each other due to mutual gravitational attraction. The momentum of each particle will increase. Statement-2: Rate of change of momentum depends upon $F_{ext}$ .

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 363: Palette 363/454

Advance MCQ

Statement-1: A concept of pseudo forces is valid both for inertial as well as non-inertial frame of reference. Statement-2: A frame accelerated with respect to an inertial frame is a non-inertial frame.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 364: Palette 364/454

Advance MCQ

Statement-1: For all bodies, momentum always remains same. Statement-2: If two bodies of different masses have same momentum the lighter body possesses greater velocity.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 365: Palette 365/454

Advance MCQ

Comprehension Passage: Comprehension - 1

A rod AB rests with the end A on rough horizontal ground and the end B against a smooth vertical wall. The rod is uniform and of weight W. If the rod is in equilibrium in the position shown in figure. Based on the above facts, answer the following questions. The frictional force at A

A

$\sqrt{3}W$

B

$\frac{\sqrt{3}W}{2}$

C

$\frac{\sqrt{3}W}{4}$

D

$\frac{\sqrt{3}W}{8}$

Question 366: Palette 366/454

Advance MCQ

Comprehension Passage: Comprehension - 1

A rod AB rests with the end A on rough horizontal ground and the end B against a smooth vertical wall. The rod is uniform and of weight W. If the rod is in equilibrium in the position shown in figure. Based on the above facts, answer the following questions. The normal reaction at $A$

A

$W$

B

$\sqrt{3} W$

C

$\frac{\sqrt{3} W}{2}$

D

$\frac{\sqrt{3} W}{4}$

Question 367: Palette 367/454

Advance MCQ

Comprehension Passage: Comprehension - 1

A rod AB rests with the end A on rough horizontal ground and the end B against a smooth vertical wall. The rod is uniform and of weight W. If the rod is in equilibrium in the position shown in figure. Based on the above facts, answer the following questions. The normal reaction at B

A

$\frac{\sqrt{3}W}{4}$

B

$\frac{\sqrt{3}W}{2}$

C

$\sqrt{3}W$

D

W

Question 368: Palette 368/454

Advance MCQ

Comprehension Passage: Comprehension - 2

A 20 kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in figure. A cable at an angle of $30^{\circ}$ with the beam helps to support the light. Based on the above facts, answer the following questions. The tension in the cable is

A

329 N

B

239 N

C

932 N

D

392 N

Question 369: Palette 369/454

Advance MCQ

Comprehension Passage: Comprehension - 2

A 20 kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in figure. A cable at an angle of $30^{\circ}$ with the beam helps to support the light. Based on the above facts, answer the following questions. The horizontal force exerted on the beam by the pole is

A

339 N, left

B

393 N, left

C

339 N, right

D

393 N, right

Question 370: Palette 370/454

Advance MCQ

Comprehension Passage: Comprehension - 2

A 20 kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in figure. A cable at an angle of $30^{\circ}$ with the beam helps to support the light. Based on the above facts, answer the following questions. The vertical force exerted on the beam by the pole is

A

zero

B

196 N, up

C

392 N, down

D

196 N, down

Question 371: Palette 371/454

Advance MCQ

Comprehension Passage: Comprehension - 3

A hemispherical bowl of radius $R = 0.1 \, m$ is rotating about its own axis (which is vertical) with an angular velocity $\omega$ . A particle of mass $10^{-2} \, kg$ on the frictionless inner surface of the bowl is also rotating with the same $\omega$ . The particle is at a height h from the bottom of the bowl. Based on the above facts, answer the following questions. The value of $\omega$ in terms of $h$ and $R$ is

A

$\sqrt{\frac{g}{R}}$

B

$\sqrt{\frac{g}{h}}$

C

$\sqrt{\frac{g}{R + h}}$

D

$\sqrt{\frac{g}{R - h}}$

Question 372: Palette 372/454

Advance MCQ

Comprehension Passage: Comprehension - 3

A hemispherical bowl of radius $R = 0.1 \, m$ is rotating about its own axis (which is vertical) with an angular velocity $\omega$ . A particle of mass $10^{-2} \, kg$ on the frictionless inner surface of the bowl is also rotating with the same $\omega$ . The particle is at a height h from the bottom of the bowl. Based on the above facts, answer the following questions. The minimum value of $\omega$ needed, in order to have a non-zero value of $h$

A

$8.8\mathrm{rads}^{-1}$

B

$7.9\mathrm{rads}^{-1}$

C

$9.9\mathrm{rads}^{-1}$

D

None of the above seems to be correct

Question 373: Palette 373/454

Advance MCQ

Comprehension Passage: Comprehension - 3

A hemispherical bowl of radius $R = 0.1 \, m$ is rotating about its own axis (which is vertical) with an angular velocity $\omega$ . A particle of mass $10^{-2} \, kg$ on the frictionless inner surface of the bowl is also rotating with the same $\omega$ . The particle is at a height h from the bottom of the bowl. Based on the above facts, answer the following questions. It is desired to measure g (acceleration due to gravity) using the set-up by measuring h accurately. Assuming that R and $\omega$ are known precisely and that the least count in the measurement of h is $10^{-4}$ m, the minimum possible error $\Delta g$ in the measured value of g is

A

$7.98 \times 10^{-3}$ ms $^{-2}$

B

$9.78 \times 10^{-3}$ ms $^{-2}$

C

$8.79 \times 10^{-3}$ ms $^{-2}$

D

$9.87 \times 10^{-3}$ ms $^{-2}$

Question 374: Palette 374/454

Advance MCQ

Comprehension Passage: Comprehension - 4

A smooth semicircular wire track of radius R is fixed in a vertical plane (shown in figure). One end of a massless spring of natural length $\frac{3R}{4}$ is attached to the lowest point O of the wire track. A small ring of mass m which can slide on the track is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes an angle $60^{\circ}$ with the vertical. The spring constant is $K = \frac{mg}{R}$ . Consider the instant when the ring is making an angle $60^{\circ}$ with the vertical. The spring is released. Based on the above facts, answer the following questions. The free body diagram of the ring for the situation talked is

A

B

C

D

Question 375: Palette 375/454

Advance MCQ

Comprehension Passage: Comprehension - 4

A smooth semicircular wire track of radius R is fixed in a vertical plane (shown in figure). One end of a massless spring of natural length $\frac{3R}{4}$ is attached to the lowest point O of the wire track. A small ring of mass m which can slide on the track is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes an angle $60^{\circ}$ with the vertical. The spring constant is $K = \frac{mg}{R}$ . Consider the instant when the ring is making an angle $60^{\circ}$ with the vertical. The spring is released. Based on the above facts, answer the following questions. The tangential acceleration of the ring

A

$\frac{\sqrt{3}}{4}g$

B

$\frac{3\sqrt{3}}{8}g$

C

$\frac{\sqrt{3}}{2}g$

D

$\frac{5\sqrt{3}}{8}g$

Question 376: Palette 376/454

Advance MCQ

Comprehension Passage: Comprehension - 4

A smooth semicircular wire track of radius R is fixed in a vertical plane (shown in figure). One end of a massless spring of natural length $\frac{3R}{4}$ is attached to the lowest point O of the wire track. A small ring of mass m which can slide on the track is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes an angle $60^{\circ}$ with the vertical. The spring constant is $K = \frac{mg}{R}$ . Consider the instant when the ring is making an angle $60^{\circ}$ with the vertical. The spring is released. Based on the above facts, answer the following questions. The normal reaction of the ring

A

$\frac{1}{8}$ mg

B

$\frac{1}{4}$ mg

C

$\frac{3}{8}$ mg

D

$\frac{1}{2}$ mg

Question 377: Palette 377/454

Advance MCQ

Comprehension Passage: Comprehension - 5

Two blocks of mass $M_{1}=10$ kg and $m_{2}=5$ kg connected to each other by a massless inextensible string of length 0.3 m are placed along a diameter of turn table. The coefficient of friction between the table and $m_{1}$ is 0.5 while there is no friction between $m_{2}$ and the table. The table is rotating with an angular velocity of $10\ rads^{-1}$ about a vertical axis passing through its centre O. The masses are placed along the diameter of table on either side of the centre O such that the mass $m_{1}$ is at a distance of 0.124 m from O. The masses are observed to be at rest with respect to an observer on the turn table. Based on the above facts, answer the following questions. The frictional force on $m_{1}$

A

18 N, outwards

B

18 N, inwards

C

36 N, outwards

D

36 N, inwards

Question 378: Palette 378/454

Advance MCQ

Comprehension Passage: Comprehension - 5

Two blocks of mass $M_{1}=10$ kg and $m_{2}=5$ kg connected to each other by a massless inextensible string of length 0.3 m are placed along a diameter of turn table. The coefficient of friction between the table and $m_{1}$ is 0.5 while there is no friction between $m_{2}$ and the table. The table is rotating with an angular velocity of $10\ rads^{-1}$ about a vertical axis passing through its centre O. The masses are placed along the diameter of table on either side of the centre O such that the mass $m_{1}$ is at a distance of 0.124 m from O. The masses are observed to be at rest with respect to an observer on the turn table. Based on the above facts, answer the following questions. The minimum angular speed of the turn table, so that the masses will slip from this position

A

$12.67 \, rads^{-1}$

B

$11.67 \, rads^{-1}$

C

$16.27 \, rads^{-1}$

D

$17.67 \, rads^{-1}$

Question 379: Palette 379/454

Advance MCQ

Comprehension Passage: Comprehension - 5

Two blocks of mass $M_{1}=10$ kg and $m_{2}=5$ kg connected to each other by a massless inextensible string of length 0.3 m are placed along a diameter of turn table. The coefficient of friction between the table and $m_{1}$ is 0.5 while there is no friction between $m_{2}$ and the table. The table is rotating with an angular velocity of $10\ rads^{-1}$ about a vertical axis passing through its centre O. The masses are placed along the diameter of table on either side of the centre O such that the mass $m_{1}$ is at a distance of 0.124 m from O. The masses are observed to be at rest with respect to an observer on the turn table. Based on the above facts, answer the following questions. How should the masses be placed from O with the spring remaining taut so that there is no frictional force acting on the mass $m_{1}$ ?

A

$m_{2}$ at a distance of 0.1 m

B

$m_{1}$ at a distance of 0.2 m

C

$m_{2}$ at a distance of 0.2 m

D

$m_{1}$ at a distance of 0.3 m

Question 380: Palette 380/454

Advance MCQ

Comprehension Passage: Comprehension - 6

Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45^{\circ}$ to the horizontal on both sides. The coefficient of friction between block A and the wedge is $\frac{2}{3}$ and that between block B and the wedge is $\frac{1}{3}$ . If the system A and B is released from rest. Based on the above facts, answer the following questions. The acceleration of $A$

A

$\frac{g}{\sqrt{2}}$

B

$\frac{g}{\sqrt{3}}$

C

$\frac{g}{2}$

D

zero

Question 381: Palette 381/454

Advance MCQ

Comprehension Passage: Comprehension - 6

Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45^{\circ}$ to the horizontal on both sides. The coefficient of friction between block A and the wedge is $\frac{2}{3}$ and that between block B and the wedge is $\frac{1}{3}$ . If the system A and B is released from rest. Based on the above facts, answer the following questions. Tension in the string

A

$\frac{\sqrt{2}}{3}$ mg

B

$\frac{2\sqrt{2}}{3}$ mg

C

$\sqrt{2}$ mg

D

$\frac{4\sqrt{2}}{3}$ mg

Question 382: Palette 382/454

Advance MCQ

Comprehension Passage: Comprehension - 6

Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45^{\circ}$ to the horizontal on both sides. The coefficient of friction between block A and the wedge is $\frac{2}{3}$ and that between block B and the wedge is $\frac{1}{3}$ . If the system A and B is released from rest. Based on the above facts, answer the following questions. The magnitude and direction of the force of friction acting on $A$

A

$\frac{Mg}{\sqrt{2}}$ , down the incline

B

$\frac{mg}{2\sqrt{2}}$ , up the incline

C

$\frac{mg}{3\sqrt{2}}$ , down the incline

D

$\frac{mg}{3\sqrt{2}}$ , up the incline

Question 383: Palette 383/454

Advance MCQ

Comprehension Passage: Comprehension - 7

In the figure masses $m_{1}$ , $m_{2}$ and M are 20 kg, 5 kg and 50 kg respectively. The coefficient of friction between M and ground is zero. The coefficient of friction between $m_{1}$ and M and that between $m_{2}$ and ground is 0.3. The pulleys and strings are massless. The string is perfectly horizontal between $P_{1}$ and $m_{1}$ and also between $P_{2}$ and $m_{2}$ . The string is perfectly vertical between $P_{1}$ and $P_{2}$ . An external horizontal force F is applied to the mass M. Let the magnitude of the force of friction between $m_{1}$ and M be $f_{1}$ and that between $m_{2}$ and ground be $f_{2}$ . Take $g = 10 \, ms^{-2}$ . Based on the above facts, answer the following questions. A free body diagram of mass M, clearly showing all the forces

A

B

C

D

None of these

Question 384: Palette 384/454

Advance MCQ

Comprehension Passage: Comprehension - 7

In the figure masses $m_{1}$ , $m_{2}$ and M are 20 kg, 5 kg and 50 kg respectively. The coefficient of friction between M and ground is zero. The coefficient of friction between $m_{1}$ and M and that between $m_{2}$ and ground is 0.3. The pulleys and strings are massless. The string is perfectly horizontal between $P_{1}$ and $m_{1}$ and also between $P_{2}$ and $m_{2}$ . The string is perfectly vertical between $P_{1}$ and $P_{2}$ . An external horizontal force F is applied to the mass M. Let the magnitude of the force of friction between $m_{1}$ and M be $f_{1}$ and that between $m_{2}$ and ground be $f_{2}$ . Take $g = 10 \, ms^{-2}$ . Based on the above facts, answer the following questions. For a particular force $F$ it is found that $f_{1} = 2f_{2}$ .

A

$f_{1} = 15\mathrm{N}$ , $f_{2} = 30\mathrm{N}$

B

$f_{1} = 30\mathrm{N}$ , $f_{2} = 60\mathrm{N}$

C

$f_{1} = 30\mathrm{N}$ , $f_{2} = 60\mathrm{N}$

D

$f_{1} = 30\mathrm{N}$ , $f_{2} = 15\mathrm{N}$

Question 385: Palette 385/454

Advance MCQ

Comprehension Passage: Comprehension - 7

In the figure masses $m_{1}$ , $m_{2}$ and M are 20 kg, 5 kg and 50 kg respectively. The coefficient of friction between M and ground is zero. The coefficient of friction between $m_{1}$ and M and that between $m_{2}$ and ground is 0.3. The pulleys and strings are massless. The string is perfectly horizontal between $P_{1}$ and $m_{1}$ and also between $P_{2}$ and $m_{2}$ . The string is perfectly vertical between $P_{1}$ and $P_{2}$ . An external horizontal force F is applied to the mass M. Let the magnitude of the force of friction between $m_{1}$ and M be $f_{1}$ and that between $m_{2}$ and ground be $f_{2}$ . Take $g = 10 \, ms^{-2}$ . Based on the above facts, answer the following questions. The value of F such that condition $f_{1}=2f_{2}$ is fulfilled is

A

60 N

B

30 N

C

45 N

D

15 N

Question 386: Palette 386/454

Advance MCQ

Comprehension Passage: Comprehension - 7

In the figure masses $m_{1}$ , $m_{2}$ and M are 20 kg, 5 kg and 50 kg respectively. The coefficient of friction between M and ground is zero. The coefficient of friction between $m_{1}$ and M and that between $m_{2}$ and ground is 0.3. The pulleys and strings are massless. The string is perfectly horizontal between $P_{1}$ and $m_{1}$ and also between $P_{2}$ and $m_{2}$ . The string is perfectly vertical between $P_{1}$ and $P_{2}$ . An external horizontal force F is applied to the mass M. Let the magnitude of the force of friction between $m_{1}$ and M be $f_{1}$ and that between $m_{2}$ and ground be $f_{2}$ . Take $g = 10 \, ms^{-2}$ . Based on the above facts, answer the following questions. Tension in the string is

A

15 N

B

16 N

C

17 N

D

18 N

Question 387: Palette 387/454

Advance MCQ

Comprehension Passage: Comprehension - 7

In the figure masses $m_{1}$ , $m_{2}$ and M are 20 kg, 5 kg and 50 kg respectively. The coefficient of friction between M and ground is zero. The coefficient of friction between $m_{1}$ and M and that between $m_{2}$ and ground is 0.3. The pulleys and strings are massless. The string is perfectly horizontal between $P_{1}$ and $m_{1}$ and also between $P_{2}$ and $m_{2}$ . The string is perfectly vertical between $P_{1}$ and $P_{2}$ . An external horizontal force F is applied to the mass M. Let the magnitude of the force of friction between $m_{1}$ and M be $f_{1}$ and that between $m_{2}$ and ground be $f_{2}$ . Take $g = 10 \, ms^{-2}$ . Based on the above facts, answer the following questions. Accelerations of the masses

A

$a_{M}=\frac{2}{5}\ ms^{-2}$ , $a_{m_{1}}=\frac{3}{5}\ ms^{-2}$ , $a_{m_{2}}=\frac{3}{5}\ ms^{-2}$

B

$a_{M}=\frac{3}{5}\ ms^{-2}$ , $a_{m_{1}}=\frac{3}{5}\ ms^{-2}$ , $a_{m_{2}}=\frac{2}{5}\ ms^{-2}$

C

$a_{M}=a_{m_{1}}=a_{m_{2}}=\frac{3}{5}~ms^{-2}$

D

$a_{M}=a_{m_{1}}=a_{m_{2}}=0$

Question 388: Palette 388/454

Advance MCQ

Comprehension Passage: Comprehension - 8

A particle moves in the xy plane under the action of a force $\vec{F}$ such that the value of its linear momentum $\vec{P}$ at any time t is $p_{x}=2\cos t$ and $p_{y}=2\sin t$ . Based on the above facts, answer the following questions. The magnitude of the force is

A

1 unit

B

2 units

C

3 units

D

4 units

Question 389: Palette 389/454

Advance MCQ

Comprehension Passage: Comprehension - 8

A particle moves in the xy plane under the action of a force $\vec{F}$ such that the value of its linear momentum $\vec{P}$ at any time t is $p_{x}=2\cos t$ and $p_{y}=2\sin t$ . Based on the above facts, answer the following questions. What is the angle between $\vec{F}$ and $\vec{p}$ ?

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$90^{\circ}$

Question 390: Palette 390/454

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Comprehension Passage: Comprehension - 8

A particle moves in the xy plane under the action of a force $\vec{F}$ such that the value of its linear momentum $\vec{P}$ at any time t is $p_{x}=2\cos t$ and $p_{y}=2\sin t$ . Based on the above facts, answer the following questions. The magnitude of the momentum is

A

1 unit

B

2 units

C

3 units

D

4 units

Question 391: Palette 391/454

Advance MCQ

Comprehension Passage: Comprehension - 9

A block of mass m slides down an inclined plane of elevation angle $\alpha$ . The incline is fixed end to end in an elevator of base length l. Assume that initially the particle is at the top of the incline. Based on the above facts, answer the following questions. When the elevator accelerates up with acceleration $a_0$ , then the acceleration of the particle with respect to the incline is

A

$g \sin \alpha$

B

$(g + a_0)\sin \alpha$

C

$a_0 \sin \alpha$

D

$g \sin \alpha + a_0 \cos \alpha$

Question 392: Palette 392/454

Advance MCQ

Comprehension Passage: Comprehension - 9

A block of mass m slides down an inclined plane of elevation angle $\alpha$ . The incline is fixed end to end in an elevator of base length l. Assume that initially the particle is at the top of the incline. Based on the above facts, answer the following questions. Consider that the elevator falls freely, in such a situation, the force exerted by the block on the elevator is

A

$mg \sin \alpha$

B

$mg \cos \alpha$

C

zero

D

None of these

Question 393: Palette 393/454

Advance MCQ

Comprehension Passage: Comprehension - 9

A block of mass m slides down an inclined plane of elevation angle $\alpha$ . The incline is fixed end to end in an elevator of base length l. Assume that initially the particle is at the top of the incline. Based on the above facts, answer the following questions. The time taken by the particle to reach the bottom of the incline, when the elevator accelerates up with acceleration $a_0$ is $T$ . Then

A

$T = \sqrt{\frac{2l}{g\sin\alpha}}$

B

$T = \sqrt{\frac{4l}{(g + a_0)\sin(2\alpha)}}$

C

$T = \sqrt{\frac{2l}{a_0\sin(2\alpha)}}$

D

$T = \sqrt{\frac{l}{(g + a_0)\sin(2\alpha)}}$

Question 394: Palette 394/454

Advance MCQ

Comprehension Passage: Comprehension - 9

A block of mass m slides down an inclined plane of elevation angle $\alpha$ . The incline is fixed end to end in an elevator of base length l. Assume that initially the particle is at the top of the incline. Based on the above facts, answer the following questions. If the elevator moves with constant velocity, then the time taken by the block to reach the bottom of the incline is

A

$\sqrt{\frac{2l}{g\sin(2\alpha)}}$

B

$\sqrt{\frac{2l}{g\cos\alpha}}$

C

$\sqrt{\frac{2l}{g}}$

D

$\sqrt{\frac{4l}{g\sin(2\alpha)}}$

Question 395: Palette 395/454

Advance MCQ

Comprehension Passage: Comprehension - 10

A block of mass m slides down a smooth incline of mass M and length l, solely as a result of the force of gravity. The incline is placed on a smooth horizontal table as shown in figure. Let us denote the coordinate system relative to the table as S and the coordinate system relative to the incline as $S'$ . The acceleration of $m$ in the $S'$ frame is

A

$\frac{(M + m)g\sin\theta}{M + m\sin^2\theta}$

B

$\frac{(M + m)g\sin\theta}{m - M\sin^2\theta}$

C

$\frac{(M - m)g\sin\theta}{M + m\sin^2\theta}$

D

$\frac{(M + m)g\sin\theta}{M + m\sin\theta}$

Question 396: Palette 396/454

Advance MCQ

Comprehension Passage: Comprehension - 10

A block of mass m slides down a smooth incline of mass M and length l, solely as a result of the force of gravity. The incline is placed on a smooth horizontal table as shown in figure. Let us denote the coordinate system relative to the table as S and the coordinate system relative to the incline as $S'$ . The acceleration of the incline in the $S$ frame

A

$\left(\frac{mg\sin\theta\cos\theta}{M - m\sin^2\theta}\right)$

B

$\left(\frac{mg\sin\theta\cos\theta}{M + m\sin^2\theta}\right)$

C

$\left(\frac{Mg\sin\theta\cos\theta}{M - m\sin^2\theta}\right)$

D

$\left(\frac{Mg\sin\theta\cos\theta}{M + m\sin^2\theta}\right)$

Question 397: Palette 397/454

Advance MCQ

Comprehension Passage: Comprehension - 10

A block of mass m slides down a smooth incline of mass M and length l, solely as a result of the force of gravity. The incline is placed on a smooth horizontal table as shown in figure. Let us denote the coordinate system relative to the table as S and the coordinate system relative to the incline as $S'$ . The force exerted by the small $m$ on the wedge of mass $M$

A

$mg \cos \theta$

B

$\frac{Mmg \cos \theta}{M + m \sin^2 \theta}$

C

$\frac{mg}{\cos \theta}$

D

None of these

Question 398: Palette 398/454

Advance MCQ

Comprehension Passage: Comprehension - 11

A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions. The coefficient of friction between the block and the inclined surface is

A

$\frac{1}{\sqrt{2}}$

B

$\frac{1}{\sqrt{3}}$

C

$\frac{1}{2}$

D

$\frac{1}{\sqrt{5}}$

Question 399: Palette 399/454

Advance MCQ

Comprehension Passage: Comprehension - 11

A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions. Contact force between the inclined plane and heavy block

A

1250 N

B

25000 N

C

5000 N

D

2500 N

Question 400: Palette 400/454

Advance MCQ

Comprehension Passage: Comprehension - 11

A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions. Tension in the string

A

250 N

B

1250 N

C

2500 N

D

5000 N

Question 401: Palette 401/454

Advance MCQ

Comprehension Passage: Comprehension - 11

A heavy block of mass 250 kg is being pulled up an inclined plane of angle $30^{\circ}$ by means of a wire passing over a pulley of radius 5 cm and connected to a motor as shown in the figure. The power output of the motor is 5 kW and the block moves up with a constant velocity of $2 \, ms^{-1}$ . Based on the information provided, answer the following questions. Frictional force acts on the block

A

12.5 N

B

125 N

C

1250 N

D

12500 N

Question 402: Palette 402/454

Advance MCQ

Comprehension Passage: Comprehension - 12

A bead of mass m is attached to one end of a spring of natural length R and spring constant $k = \frac{(\sqrt{3} + 1)mg}{R}$ . The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown in figure. Based on the information provided, answer the following questions. The normal reaction at $B$ just after it is released to move is

A

$\frac{mg}{2}$

B

$\sqrt{3} mg$

C

$3\sqrt{3} mg$

D

$\frac{3\sqrt{3} mg}{2}$

Question 403: Palette 403/454

Advance MCQ

Comprehension Passage: Comprehension - 12

A bead of mass m is attached to one end of a spring of natural length R and spring constant $k = \frac{(\sqrt{3} + 1)mg}{R}$ . The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown in figure. Based on the information provided, answer the following questions. Tangential acceleration of the bead just after it is released is

A

$\frac{g}{2}$

B

$\frac{g}{4}$

C

$\frac{2g}{3}$

D

$\frac{3g}{4}$

Question 404: Palette 404/454

Advance MCQ

Comprehension Passage: Comprehension - 13

A painter of mass 100 kg is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is 450 N. If the crate weighs 25 kg then, based on the information provided, answer the following questions. The acceleration of the system (painter + crate) is

A

$22 \, ms^{-2}$ , up

B

$2 \, ms^{-2}$ , down

C

$2 \, ms^{-2}$ , down

D

$22 \, ms^{-2}$ , down

Question 405: Palette 405/454

Advance MCQ

Comprehension Passage: Comprehension - 13

A painter of mass 100 kg is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is 450 N. If the crate weighs 25 kg then, based on the information provided, answer the following questions. The tension in the cable supporting the cabin is

A

500 N

B

1000 N

C

1250 N

D

750 N

Question 406: Palette 406/454

Advance MCQ

Comprehension Passage: Comprehension - 13

A painter of mass 100 kg is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is 450 N. If the crate weighs 25 kg then, based on the information provided, answer the following questions. Assuming the painter to be of mass $M$ , crate to be of mass $m$ , then the system will be in equilibrium when the painter holds the rope with a force given by

A

$(m + M)g$

B

$(M - m)g$

C

$\frac{1}{2}(M + m)g$

D

$\frac{1}{2}(M - m)g$

Question 407: Palette 407/454

Advance MCQ

Comprehension Passage: Comprehension - 14

A particle of mass m is suspended by the two strings a and b each of length l as shown. Based on this simple information, answer the following questions. In equilibrium, tension in the string $a$ is

A

$2mg$

B

$\sqrt{3} mg$

C

$mg$

D

$3mg$

Question 408: Palette 408/454

Advance MCQ

Comprehension Passage: Comprehension - 14

A particle of mass m is suspended by the two strings a and b each of length l as shown. Based on this simple information, answer the following questions. In equilibrium, tension in the string $b$ is

A

2mg

B

$\sqrt{3}mg$

C

mg

D

3mg

Question 409: Palette 409/454

Advance MCQ

Comprehension Passage: Comprehension - 14

A particle of mass m is suspended by the two strings a and b each of length l as shown. Based on this simple information, answer the following questions. If the string $a$ is now burned then the speed of the ball just before it collides with the wall is

A

$\sqrt{\frac{gl}{2}}$

B

$\sqrt{2gl}$

C

$\sqrt{gl}$

D

$\frac{\sqrt{gl}}{2}$

Question 410: Palette 410/454

Advance MCQ

Comprehension Passage: Comprehension - 15

The system shown in the figure is in equilibrium. The masses $m_{1}$ and $m_{2}$ are 2 kg and 8 kg respectively, the springs have spring constants $k_{1}=50\ Nm^{-1}$ and $k_{2}=70\ Nm^{-1}$ and the compression in second spring is 0.5 m. Assuming both the springs to have the same natural length, answer the following questions. The extension in first spring is

A

1.3 m

B

-0.5 m

C

0.5 m

D

0.9 m

Question 411: Palette 411/454

Advance MCQ

Comprehension Passage: Comprehension - 15

The system shown in the figure is in equilibrium. The masses $m_{1}$ and $m_{2}$ are 2 kg and 8 kg respectively, the springs have spring constants $k_{1}=50\ Nm^{-1}$ and $k_{2}=70\ Nm^{-1}$ and the compression in second spring is 0.5 m. Assuming both the springs to have the same natural length, answer the following questions. The tension in the string is

A

45 N

B

40 N

C

50 N

D

38 N

Question 412: Palette 412/454

Advance MCQ

Comprehension Passage: Comprehension - 15

The system shown in the figure is in equilibrium. The masses $m_{1}$ and $m_{2}$ are 2 kg and 8 kg respectively, the springs have spring constants $k_{1}=50\ Nm^{-1}$ and $k_{2}=70\ Nm^{-1}$ and the compression in second spring is 0.5 m. Assuming both the springs to have the same natural length, answer the following questions. The acceleration of the mass $m_{1}$ , when spring $k_{1}$ is cut, is

A

zero

B

2.5 ms $^{-2}$

C

3 ms $^{-2}$

D

None of these

Question 413: Palette 413/454

Advance MCQ

Comprehension Passage: Comprehension - 16

A block of mass $M$ is placed on a horizontal surface and it is tied through an inextensible string to a block of mass $m$ , as shown in figure. A block of mass $m_{0}$ is also placed on M. Based on the information provided, answer the following questions. If there is no friction between any two surfaces in contact, then

A

a downward acceleration of the block m is $\frac{mg}{m + m_{0} + M}$

B

the acceleration of $m_{0}$ is zero

C

the tension in the string is Mg < T < mg

D

All the above

Question 414: Palette 414/454

Advance MCQ

Comprehension Passage: Comprehension - 16

A block of mass $M$ is placed on a horizontal surface and it is tied through an inextensible string to a block of mass $m$ , as shown in figure. A block of mass $m_{0}$ is also placed on M. Based on the information provided, answer the following questions. If a friction force exist between block $M$ and the horizontal surface with the coefficient of friction $\mu$ , then the minimum value of $\mu$ (call it as $\mu_{\min}$ ) for which the block $m$ remains stationary is

A

$\frac{m}{M}$

B

$\frac{m}{M + m_0}$

C

$\frac{M + m_0}{M}$

D

$\frac{M}{M + m_0}$

Question 415: Palette 415/454

Advance MCQ

Comprehension Passage: Comprehension - 16

A block of mass $M$ is placed on a horizontal surface and it is tied through an inextensible string to a block of mass $m$ , as shown in figure. A block of mass $m_{0}$ is also placed on M. Based on the information provided, answer the following questions. If $\mu < \mu_{\min}$ (the minimum friction required to keep the block $m$ stationary), then the downward acceleration of $m$ is

A

$\left[\frac{m - \mu M}{m + M}\right]g$

B

$\left[\frac{m - \mu(m_0 + M)}{m + m_0 + M}\right]g$

C

$\left[\frac{m - \mu(m_0 + M)}{m + M}\right]g$

D

$\left[\frac{m - \mu M}{m + m_0 + M}\right]g$

Question 416: Palette 416/454

Advance MCQ

Comprehension Passage: Comprehension - 17

ABCD is a vertical frame of mass M. Two strings between block of mass m and frame are ideal and lies in vertical plane. The frame ABCD is placed on horizontal smooth surface and a horizontal force F is applied as shown. Points P and Q are in same vertical line and two strings are of equal length. Based on the above facts, answer the following questions. Minimum force F required to make both string tight is

A

$Mg \tan \theta$

B

$Mg \cot \theta$

C

$(m + M)g \tan \theta$

D

$(m + M)g \cot \theta$

Question 417: Palette 417/454

Advance MCQ

Comprehension Passage: Comprehension - 17

ABCD is a vertical frame of mass M. Two strings between block of mass m and frame are ideal and lies in vertical plane. The frame ABCD is placed on horizontal smooth surface and a horizontal force F is applied as shown. Points P and Q are in same vertical line and two strings are of equal length. Based on the above facts, answer the following questions. If the lower string is just tight then tension in the upper string is

A

$\frac{mg}{\sin\theta}$

B

$\frac{mg}{\cos\theta}$

C

$mg \sin \theta$

D

$mg \cos \theta$

Question 418: Palette 418/454

Advance MCQ

Comprehension Passage: Comprehension - 17

ABCD is a vertical frame of mass M. Two strings between block of mass m and frame are ideal and lies in vertical plane. The frame ABCD is placed on horizontal smooth surface and a horizontal force F is applied as shown. Points P and Q are in same vertical line and two strings are of equal length. Based on the above facts, answer the following questions. The value of force $F$ for which the tension in upper string becomes twice than tension in lower string is

A

$3(m + M)g\tan \theta$

B

$2(m + M)g\tan \theta$

C

$4(m + M)g\tan \theta$

D

None of these

Question 419: Palette 419/454

Advance MCQ

Comprehension Passage: Comprehension - 18

A block of mass m = 2 kg kept on a wedge of mass M = 9 kg and a horizontal force of 210 N is applied on the wedge as shown. All the surfaces are smooth and $g = 10 \, ms^{-2}$ . If initially, when the force is applied, the block m is at the bottom of wedge and if the base length of wedge is 10 m. Based on the above facts, answer the following questions. Acceleration of wedge when mass m is moving on it

A

$\frac{210}{11}$ ms $^{-2}$

B

$\frac{10}{\sqrt{2}}$ ms $^{-2}$

C

$20 \, ms^{-2}$

D

$10\sqrt{2} \, ms^{-2}$

Question 420: Palette 420/454

Advance MCQ

Comprehension Passage: Comprehension - 18

A block of mass m = 2 kg kept on a wedge of mass M = 9 kg and a horizontal force of 210 N is applied on the wedge as shown. All the surfaces are smooth and $g = 10 \, ms^{-2}$ . If initially, when the force is applied, the block m is at the bottom of wedge and if the base length of wedge is 10 m. Based on the above facts, answer the following questions. Speed of block $m$ with respect to wedge when it reaches the top of wedge is

A

$\frac{210}{11} \mathrm{~ms}^{-1}$

B

$\frac{10}{\sqrt{2}} \mathrm{~ms}^{-1}$

C

$10\sqrt{2} \mathrm{~ms}^{-1}$

D

$20 \mathrm{~ms}^{-1}$

Question 421: Palette 421/454

Advance MCQ

Comprehension Passage: Comprehension - 18

A block of mass m = 2 kg kept on a wedge of mass M = 9 kg and a horizontal force of 210 N is applied on the wedge as shown. All the surfaces are smooth and $g = 10 \, ms^{-2}$ . If initially, when the force is applied, the block m is at the bottom of wedge and if the base length of wedge is 10 m. Based on the above facts, answer the following questions. Distance moved by wedge when block m leaves the wedge from it top is

A

$10\sqrt{2}$ m

B

$20\sqrt{2}$ m

C

20 m

D

40 m

Question 422: Palette 422/454

Advance MCQ

Comprehension Passage: Comprehension - 19

An external force F is applied at an angle $\theta$ with the horizontal as shown on the block of mass m. The coefficient of friction between block and wall is $\mu$ . Based on the above facts, answer the following questions. The minimum value of force $f$ required to keep the block at rest is

A

$\frac{mg}{\mu\cos\theta}$

B

$\frac{mg}{\sin\theta + \mu\cos\theta}$

C

$\frac{mg}{\sin\theta - \mu\cos\theta}$

D

$\frac{mg}{\mu\tan\theta}$

Question 423: Palette 423/454

Advance MCQ

Comprehension Passage: Comprehension - 19

An external force F is applied at an angle $\theta$ with the horizontal as shown on the block of mass m. The coefficient of friction between block and wall is $\mu$ . Based on the above facts, answer the following questions. The maximum value of force F up to which block remains at rest is

A

$\frac{mg}{\mu\cos\theta}$

B

$\frac{mg}{\sin\theta + \mu\cos\theta}$

C

$\frac{mg}{\sin\theta - \mu\cos\theta}$

D

$\frac{mg}{\mu\tan\theta}$

Question 424: Palette 424/454

Advance MCQ

Comprehension Passage: Comprehension - 19

An external force F is applied at an angle $\theta$ with the horizontal as shown on the block of mass m. The coefficient of friction between block and wall is $\mu$ . Based on the above facts, answer the following questions. The value of force $F$ for which friction force between block and wall is zero

A

mg

B

$\frac{mg}{\sin\theta}$

C

$\frac{mg}{\cos\theta}$

D

$\frac{mg}{\tan\theta}$

Question 425: Palette 425/454

Advance MCQ

Comprehension Passage: Comprehension - 20

Two blocks of masses 10 kg and 20 kg are moving together with a constant speed of $20 \, ms^{-1}$ and 10 kg block is not slipping on 20 kg when blocks are moving in region AB which is horizontal and smooth. The coefficient of friction between the blocks is $\mu_{1}=0.5$ . The horizontal surface BC is rough and coefficient of friction between 20 kg block and surface BC is $\mu_{2}$ . Taking $g=10\ ms^{-2}$ , answer the following questions. When the blocks are moving on the smooth horizontal region AB of surface, then

A

frictional force on 10 kg block is zero

B

frictional force on 10 kg block is 50 N

C

frictional force on 10 kg block is less than 50 N but non zero

D

None of these

Question 426: Palette 426/454

Advance MCQ

Comprehension Passage: Comprehension - 20

Two blocks of masses 10 kg and 20 kg are moving together with a constant speed of $20 \, ms^{-1}$ and 10 kg block is not slipping on 20 kg when blocks are moving in region AB which is horizontal and smooth. The coefficient of friction between the blocks is $\mu_{1}=0.5$ . The horizontal surface BC is rough and coefficient of friction between 20 kg block and surface BC is $\mu_{2}$ . Taking $g=10\ ms^{-2}$ , answer the following questions. When this system of blocks enters the rough horizontal surface BC then still 10 kg block is not slipping on 20 kg block, then

A

maximum value of $\mu_{2}$ is 0.5

B

maximum value of $\mu_{2}$ is 0.75

C

total kinetic friction is 100 N acting on 20 kg block for the above maximum value of $\mu_{2}$

D

total frictional force on 20 kg block is 150 N

Question 427: Palette 427/454

Advance MCQ

Comprehension Passage: Comprehension - 20

Two blocks of masses 10 kg and 20 kg are moving together with a constant speed of $20 \, ms^{-1}$ and 10 kg block is not slipping on 20 kg when blocks are moving in region AB which is horizontal and smooth. The coefficient of friction between the blocks is $\mu_{1}=0.5$ . The horizontal surface BC is rough and coefficient of friction between 20 kg block and surface BC is $\mu_{2}$ . Taking $g=10\ ms^{-2}$ , answer the following questions. If the value of $\mu_{2} = 0.2$ , then in 15 seconds after the blocks have entered the rough surface

A

The distance travelled by them in rough surface is 75 m

B

The distance travelled by them in rough surface is 100 m

C

Total force applied by 10 kg on 20 kg block is 102 N after 15 seconds

D

None of these

Question 428: Palette 428/454

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Comprehension Passage: Comprehension - 21

A block is rotating in a circular track and angular speed of the block is given $\omega = at^{2}$ , where $\omega$ is in rads $^{-1}$ and t is in seconds, a is a constant and equal to 2 rads $^{-3}$ . Mass of the block is 1 kg. Radius of circular track is 1 m. Based on the above facts, answer the following questions. Net force acting on the block at = 2 s is

A

8 N

B

$8\sqrt{17}$ N

C

32 N

D

4 N

Question 429: Palette 429/454

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Comprehension Passage: Comprehension - 21

A block is rotating in a circular track and angular speed of the block is given $\omega = at^{2}$ , where $\omega$ is in rads $^{-1}$ and t is in seconds, a is a constant and equal to 2 rads $^{-3}$ . Mass of the block is 1 kg. Radius of circular track is 1 m. Based on the above facts, answer the following questions. Angle between velocity vector and acceleration vector is

A

less than $90^{\circ}$

B

greater than $90^{\circ}$

C

equal to $90^{\circ}$

D

data is insufficient

Question 430: Palette 430/454

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Comprehension Passage: Comprehension - 21

A block is rotating in a circular track and angular speed of the block is given $\omega = at^{2}$ , where $\omega$ is in rads $^{-1}$ and t is in seconds, a is a constant and equal to 2 rads $^{-3}$ . Mass of the block is 1 kg. Radius of circular track is 1 m. Based on the above facts, answer the following questions. Time at which rate of change of speed is equal to $\frac{1}{\sqrt{2}}$ times the net acceleration is

A

$\frac{1}{2}$ s

B

1 s

C

2 s

D

4 s

Question 431: Palette 431/454

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Comprehension Passage: Comprehension - 22

All pulleys and strings shown in figure are light and there is no friction in any string and pulley. Based on the above facts, answer the following questions. Maximum mass m to be hanged so that system remain in equilibrium

A

8 kg

B

9.6 kg

C

6.4 kg

D

10 kg

Question 432: Palette 432/454

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Comprehension Passage: Comprehension - 22

All pulleys and strings shown in figure are light and there is no friction in any string and pulley. Based on the above facts, answer the following questions. Mass m to be hanged so that none of the block remains in equilibrium must satisfy

A

m > 8 kg

B

m > 9.6 kg

C

m > 10 kg

D

m > 12 kg

Question 433: Palette 433/454

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Comprehension Passage: Comprehension - 22

All pulleys and strings shown in figure are light and there is no friction in any string and pulley. Based on the above facts, answer the following questions. Acceleration of hanging block if mass of hanging block is 9 kg

A

$\frac{9}{31}$ ms $^{-2}$

B

$\frac{10}{31}$ ms $^{-2}$

C

$\frac{10}{41}$ ms $^{-2}$

D

$\frac{11}{32}$ ms $^{-2}$

Question 434: Palette 434/454

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Comprehension Passage: Comprehension - 23

In the situation shown below, a block of mass m is kept over wedge of mass M. Spring constant of spring shown in figure is k. All surfaces are frictionless. Based on the above facts, answer the following questions. Compression in spring is equal to

A

$\frac{mg}{k}$

B

$\frac{mg\cos\theta}{k}$

C

$\frac{mg\sin 2\theta}{2k}$

D

$\frac{mg\cos^2\theta}{2k}$

Question 435: Palette 435/454

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Comprehension Passage: Comprehension - 23

In the situation shown below, a block of mass m is kept over wedge of mass M. Spring constant of spring shown in figure is k. All surfaces are frictionless. Based on the above facts, answer the following questions. Force on ground due to wedge is

A

Mg

B

$(M + m)g$

C

$(m\cos\theta + M)g$

D

$(m\cos^{2}\theta + M)g$

Question 436: Palette 436/454

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Comprehension Passage: Comprehension - 23

In the situation shown below, a block of mass m is kept over wedge of mass M. Spring constant of spring shown in figure is k. All surfaces are frictionless. Based on the above facts, answer the following questions. Net force on block is equal to

A

$mg \sin \theta$

B

$mg(\cos \theta + 1)$

C

$mg \cos \theta$

D

mg

Question 437: Palette 437/454

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Comprehension Passage: Comprehension - 24

Two blocks of masses 25 kg and 5 kg are placed on horizontal table as shown in the figure. A massless string passes over a frictionless pulley whose one end is connected to 25 kg block and other end is connected to block M. The coefficient of friction between two blocks is $\mu = 0.3$ and between 5 kg block and ground is zero. The system is released from rest. Based on the above facts, answer the following questions. (Take $g = 10 \, \mathrm{ms}^{-2}$ ) If $M = 45 \mathrm{~kg}$ force of friction between the blocks will be

A

$80 \mathrm{~N}$

B

$60 \mathrm{~N}$

C

$30 \mathrm{~N}$

D

$75 \mathrm{~N}$

Question 438: Palette 438/454

Advance MCQ

Comprehension Passage: Comprehension - 24

Two blocks of masses 25 kg and 5 kg are placed on horizontal table as shown in the figure. A massless string passes over a frictionless pulley whose one end is connected to 25 kg block and other end is connected to block M. The coefficient of friction between two blocks is $\mu = 0.3$ and between 5 kg block and ground is zero. The system is released from rest. Based on the above facts, answer the following questions. (Take $g = 10 \, \mathrm{ms}^{-2}$ ) Value of M for which there is slipping between the blocks is

A

>90 kg

B

M>0

C

<90 kg

D

None of these

Question 439: Palette 439/454

Advance MCQ

Comprehension Passage: Comprehension - 24

Two blocks of masses 25 kg and 5 kg are placed on horizontal table as shown in the figure. A massless string passes over a frictionless pulley whose one end is connected to 25 kg block and other end is connected to block M. The coefficient of friction between two blocks is $\mu = 0.3$ and between 5 kg block and ground is zero. The system is released from rest. Based on the above facts, answer the following questions. (Take $g = 10 \, \mathrm{ms}^{-2}$ ) If $M = 45 \mathrm{~kg}$ , acceleration of $5 \mathrm{~kg}$ block will be

A

$6 \mathrm{~ms}^{-2}$

B

$5 \mathrm{~ms}^{-2}$

C

$8 \mathrm{~ms}^{-2}$

D

$10 \mathrm{~ms}^{-2}$

Question 440: Palette 440/454

Advance MCQ

Comprehension Passage: Comprehension - 25

A block of mass m revolving in a circular path of radius r with a non-uniform speed of particle. Speed of particle is given by v = kt, where k is constant. Time starts from t = 0 s. Based on the above facts, answer the following questions. At $t = t_1$ , magnitude of tangential acceleration is equal to magnitude of centripetal acceleration. Then $t_1$ is equal to

A

$\frac{r}{k}$

B

$rk$

C

$\sqrt{\frac{r}{k}}$

D

$\sqrt{\frac{k}{r}}$

Question 441: Palette 441/454

Advance MCQ

Comprehension Passage: Comprehension - 25

A block of mass m revolving in a circular path of radius r with a non-uniform speed of particle. Speed of particle is given by v = kt, where k is constant. Time starts from t = 0 s. Based on the above facts, answer the following questions. Magnitude of net force on the particle at $t = t_{1}$ is

A

2mk

B

$\sqrt{2}mk$

C

mk

D

$\frac{mk}{2}$

Question 442: Palette 442/454

Advance MCQ

Comprehension Passage: Comprehension - 25

A block of mass m revolving in a circular path of radius r with a non-uniform speed of particle. Speed of particle is given by v = kt, where k is constant. Time starts from t = 0 s. Based on the above facts, answer the following questions. The angle between net acceleration vector and radius vector at $t = \frac{2}{\sqrt{3}} t_1$ is

A

53°

B

37°

C

127°

D

137°

Question 443: Palette 443/454

Advance MCQ

Comprehension Passage: Comprehension - 26

A man of mass 50 kg is standing on a platform of mass 30 kg kept on a horizontal surface. Mass of block is 160 kg. Distance between block and pulley P is 6 m. There is no friction between block and platform. The man pulls the string with constant force 40 N. Based on the above facts, answer the following questions. Assuming no friction between platform and surface, time taken by block to reach pulley is

A

$2\sqrt{3}$ s

B

2 s

C

$3\sqrt{2}$ s

D

3 s

Question 444: Palette 444/454

Advance MCQ

Comprehension Passage: Comprehension - 26

A man of mass 50 kg is standing on a platform of mass 30 kg kept on a horizontal surface. Mass of block is 160 kg. Distance between block and pulley P is 6 m. There is no friction between block and platform. The man pulls the string with constant force 40 N. Based on the above facts, answer the following questions. Length of string pulled by man in 1 s is

A

2 m

B

6 m

C

8 m

D

12 m

Question 445: Palette 445/454

Advance MCQ

Comprehension Passage: Comprehension - 26

A man of mass 50 kg is standing on a platform of mass 30 kg kept on a horizontal surface. Mass of block is 160 kg. Distance between block and pulley P is 6 m. There is no friction between block and platform. The man pulls the string with constant force 40 N. Based on the above facts, answer the following questions. The minimum coefficient between platform and the surface so that it doesn't slip on the surface

A

0.05

B

0.1

C

0.53

D

None of these

Question 446: Palette 446/454

Advance MCQ

Comprehension Passage: Comprehension - 27

It is observed that sometimes the frictional force opposing the motion of a body is not constant but increases with speed of the body. One of the familiar example is the air resistance on a freely falling body. For small speeds this resisting force is approximately proportional to the speed. The equations of motion are not directly applied in such cases if variable force. Based on the above facts, answer the following questions. The variation of the position of a body falling freely through air can be best represented graphically by (consider y = 0 at the highest point)

A

B

C

D

Question 447: Palette 447/454

Advance MCQ

Comprehension Passage: Comprehension - 27

It is observed that sometimes the frictional force opposing the motion of a body is not constant but increases with speed of the body. One of the familiar example is the air resistance on a freely falling body. For small speeds this resisting force is approximately proportional to the speed. The equations of motion are not directly applied in such cases if variable force. Based on the above facts, answer the following questions. A 5 kg mass freely falling experiences a retarding force of 5v where v is the speed in $ms^{-1}$ has

A

5

B

10

C

15

D

20

Question 448: Palette 448/454

Advance MCQ

Comprehension Passage: Comprehension - 27

It is observed that sometimes the frictional force opposing the motion of a body is not constant but increases with speed of the body. One of the familiar example is the air resistance on a freely falling body. For small speeds this resisting force is approximately proportional to the speed. The equations of motion are not directly applied in such cases if variable force. Based on the above facts, answer the following questions. The variation of velocity with time is best represented by

A

B

C

D

Question 449: Palette 449/454

Advance MCQ

Comprehension Passage: Comprehension - 28

As shown two block of mass $m_{1}=2$ kg and $m_{2}=4$ kg are connected by an ideal spring of force constant $k=1000\ Nm^{-1}$ and the system is kept on a smooth inclined plane inclined at $\theta=30^{\circ}$ with horizontal. A third block of mass $m_{3}=1$ kg is attached to $m_{2}$ by an ideal string. A force F=15 N is applied on $m_{1}$ and the system is released from rest. Assume that the spring was initially unstretched. $(g=10\ ms^{-2})$ . Based on the above facts, answer the following questions. The common acceleration of blocks $m_{1}, m_{2}$ and $m_{3}$ is

A

$\frac{25}{7} \mathrm{~ms}^{-2}$

B

$\frac{35}{7} \mathrm{~ms}^{-2}$

C

$\frac{15}{7} \mathrm{~ms}^{-2}$

D

$\frac{7}{25} \mathrm{~ms}^{-2}$

Question 450: Palette 450/454

Advance MCQ

Comprehension Passage: Comprehension - 28

As shown two block of mass $m_{1}=2$ kg and $m_{2}=4$ kg are connected by an ideal spring of force constant $k=1000\ Nm^{-1}$ and the system is kept on a smooth inclined plane inclined at $\theta=30^{\circ}$ with horizontal. A third block of mass $m_{3}=1$ kg is attached to $m_{2}$ by an ideal string. A force F=15 N is applied on $m_{1}$ and the system is released from rest. Assume that the spring was initially unstretched. $(g=10\ ms^{-2})$ . Based on the above facts, answer the following questions. Maximum elongation in spring is

A

1 cm

B

2.4 cm

C

3.6 cm

D

4.8 cm

Question 451: Palette 451/454

Advance MCQ

Comprehension Passage: Comprehension - 28

As shown two block of mass $m_{1}=2$ kg and $m_{2}=4$ kg are connected by an ideal spring of force constant $k=1000\ Nm^{-1}$ and the system is kept on a smooth inclined plane inclined at $\theta=30^{\circ}$ with horizontal. A third block of mass $m_{3}=1$ kg is attached to $m_{2}$ by an ideal string. A force F=15 N is applied on $m_{1}$ and the system is released from rest. Assume that the spring was initially unstretched. $(g=10\ ms^{-2})$ . Based on the above facts, answer the following questions. Acceleration of $m_{3}$ when spring has maximum elongation is (approx.)

A

$1.2 \, ms^{-2}$

B

$2 \, ms^{-2}$

C

$1 \, ms^{-2}$

D

$1.5 \, ms^{-2}$

Question 452: Palette 452/454

Advance Match the Columns

Configuration of L shaped block B of mass 6 kg and two other blocks are shown. System is set free to move. At any moment, match the following parameters. $\left(g = 10 \, \text{ms}^{-2}\right)$ .

Column-I

Column-I	Column-II
(A) Friction force between block A and B (B) Tension in the string (C) Normal reaction on block A by block B (D) Normal reaction on block B by table	(P) 50 N (Q) 70 N (R) 60 N (S) 10 N (T) 20 N

A

B

C

D

Question 453: Palette 453/454

Advance MCQ

A particle of mass $m$ is at rest at the origin at time $t = 0$ . It is subjected to a force $F(t) = F_0 e^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

A

B

C

D

Question 454: Palette 454/454

Advance MCQ

The figure shows the position-time $(x - t)$ graph of one-dimensional motion of a body of mass $0.4\mathrm{kg}$ . The magnitude of each impulse is

A

0.2 Ns

B

0.4 Ns

C

0.8 Ns

D

1.6 Ns