Question 1: Palette 1/136

Allen JEE (Main) 2023 MCQ

As per given figure, a weightless pulley P is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if $g = 10 \, m/s^{2}$ )

A

$(4\sqrt{3} + 1)N$

B

$4(\sqrt{3} + 1)N$

C

$4(\sqrt{3} - 1)N$

D

$(4\sqrt{3} - 1)N$

Question 2: Palette 2/136

Allen JEE (Main) 2023 MCQ

As shown in figure, a 70 kg garden roller is pushed with a force of $\vec{F} = 200\mathrm{N}$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g = 10~ms^{-2}$ )

A

$800\sqrt{2} N$

B

$600N$

C

800N

D

$200\sqrt{3} N$

Question 3: Palette 3/136

Allen JEE (Main) 2023 MCQ

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $30^{\circ}$ , with horizontal. For $\mu_{s} = 0.25$ , the block will just start to move for the value of F: [Given g = 10 ms $^{-2}$ ]

A

$33.3N$

B

$25.2N$

C

$20N$

D

$35.7N$

Question 4: Palette 4/136

Allen JEE (Main) 2023 MCQ

Consider a block kept on an inclined plane (inclined at $45^{\circ}$ ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane ( $\mu$ ) is equal to :

A

0.33

B

0.60

C

0.25

D

0.50

Question 5: Palette 5/136

Allen JEE (Advanced) 2023 MCQ

A particle of mass m is moving in the xy-plane such that its velocity at a point $(x, y)$ is given as $\vec{v} = \alpha(y\hat{x} + 2x\hat{y})$ , where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

A

$\vec{F} = 2m\alpha^{2}(x\hat{x} +y\hat{y})$

B

$\vec{F} = m\alpha^{2}(y\hat{x} + 2x\hat{y})$

C

$\vec{F} = 2m\alpha^{2}(y\hat{x} +x\hat{y})$

D

$\vec{F} = m\alpha^{2}(x\hat{x} + 2y\hat{y})$

Question 6: Palette 6/136

Allen JEE (Main) 2022 MCQ

In the arrangement shown in figure $a_{1}, a_{2}, a_{3}$ and $a_{4}$ are the accelerations of masses $m_{1}, m_{2}, m_{3}$ and $m_{4}$ respectively. Which of the following relation is true for this arrangement?

A

$4a_{1} + 2a_{2} + a_{3} + a_{4} = 0$

B

$a_1 + 4a_2 + 3a_3 + a_4 = 0$

C

$a_{1} + 4a_{2} + 3a_{3} + 2a_{4} = 0$

D

$2a_{1} + 2a_{2} + 3a_{3} + a_{4} = 0$

Question 7: Palette 7/136

Allen JEE (Main) 2021 MCQ

A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F_0 \left[ 1 - \left( \frac{t - T}{T} \right)^2 \right]$ Where $F_{0}$ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

A

$2F_{0}T/M$

B

$F_{0}T/2M$

C

$4F_{0}T/3M$

D

$F_{0}T/3M$

Question 8: Palette 8/136

Allen JEE (Main) 2021 MCQ

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \, kg$ , $M = 16 \, kg$ Assume all the surfaces shown in the figure to be frictionless.

A

$\frac{4}{3} g$

B

$\frac{6}{5} g$

C

$\frac{3}{5} g$

D

$\frac{2}{3} g$

Question 9: Palette 9/136

Allen JEE (Main) 2021 MCQ

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (Use g = 10 m/s $^{2}$ )

A

0.34 s

B

0.2 s

C

0.25 s

D

0.4 s

Question 10: Palette 10/136

Allen JEE (Main) 2020 MCQ

An insect is at the bottom of a hemispherical ditch of radius 1m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: $(g = 10 \, ms^{-2})$

A

0.80 m

B

0.60 m

C

0.45 m

D

0.20 m

Question 11: Palette 11/136

Allen JEE (Main) 2020 MCQ

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then F equals: (Take $g = 10 \, ms^{-2}$ and the rope to be massless)

A

100 N

B

90 N

C

75 N

D

70 N

Question 12: Palette 12/136

Allen JEE (Main) 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 $g = 10 \, m/s^{2}$ )

A

$16N$

B

$40N$

C

$12N$

D

$8N$

Question 13: Palette 13/136

Allen JEE (Main) 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, $\upsilon$ 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

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

C

$\frac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\frac{2\gamma}{g}}V_{0}\right)$

D

$\frac{1}{\sqrt{\gamma g}}\ln\left(1+\sqrt{\frac{\gamma}{g}}V_{0}\right)$

Question 14: Palette 14/136

Allen JEE (Main) 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 $k_{1}/k_{2}$ of the corresponding force constants, $k_{1}$ and $k_{2}$ will be :

A

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

B

$n^2$

C

$\frac{1}{n}$

D

$n$

Question 15: Palette 15/136

Allen JEE (Main) 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

27.3 kg

B

43.3 kg

C

10.3 kg

D

18.3 kg

Question 16: Palette 16/136

Allen JEE (Main) 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 $\mu_{\mathrm{min}}$ between the mass and the inclined surface such that the mass does not move is:

A

$2\tan \theta$

B

$3\tan \theta$

C

$\tan \theta$

D

$\tan 2\theta$

Question 17: Palette 17/136

Allen JEE (Main) 2015 MCQ

Given in the figure are two blocks A and B of weight 20N and 100N, 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 N

B

150 N

C

100 N

D

80 N

Question 18: Palette 18/136

Allen JEE (Main) 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

$\frac{1}{3}m$

B

$\frac{1}{2}m$

C

$\frac{1}{6}m$

D

$\frac{2}{3}m$

Question 19: Palette 19/136

Allen JEE (Advanced) 2014 Match the Columns

A block of mass $m_{1} = 1kg$ another mass $m_{2} = 2kg$ , are placed together (see 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 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°) ≈ 0.1 ; tan(11.5°) ≈ 0.2 ; tan (16.5°) ≈ 0.3]

Column-I	Column-II
(P) $m_{2}g \sin \theta$ (Q) $(m_{1} + m_{2})g\sin \theta$ (R) $\mu m_{2}g\cos \theta$ (S) $\mu (m_1 + m_2)g\cos \theta$	(I) $\theta = 5^{\circ}$ (II) $\theta = 10^{\circ}$ (III) $\theta = 15^{\circ}$ (IV) $\theta = 20^{\circ}$

A

I-P, II-P, III-P, IV-R

B

I-Q, II-Q, III-Q, IV-R

C

I-Q, II-Q, III-Q, IV-S

D

I-Q, II-Q, III-R, IV-R

Question 20: Palette 20/136

Allen 2000 MCQ

A truck carries a 2 Ton block on a level horizontal road. The coefficient of static and kinetic frictions between the stone-block and truck-bed are 0.4 and 0.2 respectively. When the truck accelerates at $2m/s^{2}$ , how much friction acts between the stone-block and the truck-bed? $[g = 10\ m/s^{2}]$

A

2000 N

B

4000 N

C

8000 N

D

$10000N$

Question 21: Palette 21/136

Allen MCQ

A ball of mass m kept at the corner as shown in the figure, is acted by a horizontal force F. The correct free body diagram of ball is

A

B

C

D

Question 22: Palette 22/136

Allen MCQ

A girl pushes her physics book up against the horizontal ceiling of her room as shown in the figure. The book weighs 20 N and she pushes upwards with a force of 25 N. The choices below Column the magnitudes of the contact force $F_{CB}$ between the ceiling and the book, and $F_{BH}$ between the book and her hand. Select the correct pair.

A

$F_{CB} = 20N$ and $F_{BH} = 25N$

B

$F_{CB} = 25N$ and $F_{BH} = 45N$

C

$F_{CB} = 5N$ and $F_{BH} = 25N$

D

$F_{CB} = 5N$ and $F_{BH} = 45N$

Question 23: Palette 23/136

Allen MCQ

Two astronauts A and B connected with a rope stay stationary in free space relative to their spaceship. Mass of A is more than that of B and the rope is straight. Astronaut A starts pulling the rope but astronaut B does not. If you were the third astronaut in the spaceship, what do you observe?

A

Astronaut B accelerates towards A and A remains stationery.

B

Both accelerate towards each other with equal accelerations of equal modulus.

C

Both accelerate towards each other but acceleration of B is greater than that of A.

D

Both accelerate towards each other but acceleration of B is smaller than that of A.

Question 24: Palette 24/136

Allen MCQ

Under what condition(s) will an object be in equilibrium?

A

Only if it is at rest

B

Only if it is moving with constant velocity

C

Only if it is moving with constant acceleration

D

If it is either at rest or moving with constant velocity

Question 25: Palette 25/136

Allen MCQ

All three blocks placed on horizontal surface at rest than net force on the middle block is?

A

$30N$

B

$40N$

C

$90N$

D

$0N$

Question 26: Palette 26/136

Allen MCQ

In a given figure system is in equilibrium. If $W_{1} = 300 \, N$ . Then $W_{2}$ is approximately equal to

A

$500 N$

B

$400N$

C

$670N$

D

$300N$

Question 27: Palette 27/136

Allen MCQ

Normal force acting between the blocks will be:

A

$\frac{F}{3}$

B

$\frac{F}{6}$

C

$\frac{F}{4}$

D

$\frac{2F}{3}$

Question 28: Palette 28/136

Allen MCQ

Two balls A and B weighing 7 N and 9 N are connected by a light cord. The system is suspended from a fixed support by connecting the ball A with another light cord. The ball B is pulled aside by a horizontal force 12 N and equilibrium is established. Angles $\alpha$ and $\beta$ respectively are

A

$30^{\circ}$ and $60^{\circ}$ and
$6 0 ^ {\circ}$

B

$6 0 ^ {\circ}$ and $3 0 ^ {\circ}$

C

$37^{\circ}$ and $53^{\circ}$

D

$53^{\circ}$ and $37^{\circ}$

Question 29: Palette 29/136

Allen MCQ

Two masses m and M are attached to strings as shown in the figure. In equilibrium $\tan \theta$ is :

A

$1+(2M/m)$

B

$1 + (2m / M)$

C

$1 + (M / 2m)$

D

None of these

Question 30: Palette 30/136

Allen MCQ

A perfect smooth sphere A of mass 2 kg is in contact with a rectangular block B of mass 4 kg and vertical wall as shown in the figure. All surfaces are smooth. Find normal reaction by vertical wall on sphere A

A

$20N$

B

$25N$

C

$80N$

D

$45N$

Question 31: Palette 31/136

Allen MCQ

In a hemispherical bowl of radius 8R, two balls of mass 5 kg are placed in the equilibrium. Radius of the ball is 3R. Normal contact force between the two balls is given by

A

$\frac{75}{2}$

B

$\frac{75}{4}$

C

$\frac{75}{6}$

D

15

Question 32: Palette 32/136

Allen MCQ

Three identical blocks each of mass 20kg are connected by ideal strings and are being pulled along a horizontal frictionless table by a constant horizontal force F as shown in figure. What is the magnitude of force F if the tension in the string connecting blocks A and B is 60 N?

A

60 N

B

120 N

C

180 N

D

90 N

Question 33: Palette 33/136

Allen MCQ

A block of mass m is placed in contact with one end of a smooth tube of mass M (see figure). A horizontal force F acts on the tube in each case (i) and (ii). Then mark incorrect option :

A

$a_{m} = 0$ and $a_{M} = \frac{F}{M}$ in (i)

B

$a_{m} = a_{M} = \frac{F}{M + m}$ in (i)

C

$a_{m} = a_{M} = \frac{F}{M + m}$ in (ii)

D

Force on m is $\frac{mF}{M+m}$ in (ii)

Question 34: Palette 34/136

Allen MCQ

The arrangement shown in the figure is in equilibrium. What is the contact force (in N) between the block A and 2 kg block? $(g = 10 \, m/s^{2})$

A

$70N$

B

$100N$

C

$30N$

D

$50N$

Question 35: Palette 35/136

Allen MCQ

What should be the value of "m" so that 4kg block remains at rest :-

A

3 kg

B

4 kg

C

1.5 kg

D

2.5 kg

Question 36: Palette 36/136

Allen MCQ

Mark the INCORRECT statement(s): Magnitude of acceleration of both blocks is $8 \, m/s^{2}$

A

tension in the string is 180 N

B

acceleration of mass $10 \, kg$ is $8 \, m/s^{2}$ upward

C

acceleration of mass $10 \, kg$ is $8 \, m/s^{2}$ downward

D

acceleration of mass $40 \, kg$ is $8 \, m/s^{2}$ downward

Question 37: Palette 37/136

Allen MCQ

All pulleys and strings are massless, for what ratio of $m_{1}: m_{2}: m_{3}$ system will be in equilibrium (inclined is frictionless)

A

1:2:1

B

2:2:1

C

1:2:2

D

2:1:2

Question 38: Palette 38/136

Allen MCQ

A force F is applied to the initially stationary cart. The variation of force with time is shown in the figure. The speed of cart at t = 5 second is :-

A

$10 \mathrm{~m} / \mathrm{s}$

B

8.33 m/s

C

2 m/s

D

zero

Question 39: Palette 39/136

Allen MCQ

Curve between net force vs time is shown.-Initially particle is at rest. Which of the following best represents the resulting velocity - time graph of the particle?

A

B

C

D

Question 40: Palette 40/136

Allen MCQ

In a given figure a block is kept on the fixed wedge. A force of magnitude F is acting on the block such that it makes angle $\theta$ with the inclined plane. Now $\theta$ is changing from 0 to 180° then graph between normal reaction between block and wedge (N) and $\theta$ is :-

A

B

C

D

Question 41: Palette 41/136

Allen MCQ

A smooth pulley P of mass M = 2 kg is lying on a smooth table. A light string passes round the pulley and has mass m = 1kg and $m' = 2kg$ attached to its ends, the two portions of the string being perpendicular to the edge of the table so that the masses hang vertically. Acceleration of pulley is-

A

$\frac{g}{2}$

B

$\frac{2g}{3}$

C

$\frac{4g}{9}$

D

$\frac{4g}{7}$

Question 42: Palette 42/136

Allen MCQ

With what acceleration 'a' shown the elevator descends so that the block of mass M exerts a force of $\frac{Mg}{10}$ on the weighing machine? [g = acceleration due to gravity]

A

0.3 g

B

0.1 g

C

0.9 g

D

0.6 g

Question 43: Palette 43/136

Allen MCQ

The wedge of mass M sits at rest on a scale as shown in figure. A small block of mass m slides down the frictionless incline of the wedge. The scale reading while the block slides, is

A

$(m + M) g$

B

$M g + m g \cos^ {2} \theta$

C

$(m + M)g + mg\sin^2\theta$

D

$(M - m) g + m g \sin^ {2} \theta$

Question 44: Palette 44/136

Allen MCQ

The block is released from rest with the unstretched positions of springs initially. The acceleration of the block just after released will be $(g = 10 \, m/s^{2})$

A

Zero

B

$10m / s^2$ upwards

C

$10m / s^2$ downward

D

$5m / s^2$ upwards

Question 45: Palette 45/136

Allen MCQ

A sphere of mass 'm' is kept in equilibrium with the help of several springs as shown in the figure. Measurements show that one of the springs applies a force $\vec{F}$ on the sphere. With what acceleration the sphere will move immediately after this particular spring is cut?

A

Zero

B

$\frac{\vec{F}}{m}$

C

$-\frac{\vec{F}}{m}$

D

Insufficient information

Question 46: Palette 46/136

Allen MCQ

Two blocks A and B of equal mass 2 kg are arranged as shown with springs $S_{1}$ and $S_{2}$ . Spring $S_{2}$ is pulled with force F = 6 N. Acceleration of block B is 4 m/s $^{2}$ towards right at an instant. If F is suddenly removed at this instant, the instantaneous acceleration of A and B will be (Assume no friction)

A

$a_{A} = 1 \, m/s^{2}$ towards right and $a_{B} = 4 \, m/s^{2}$ left

B

$a_{A} = 1 \, m/s^{2}$ towards left and $a_{B} = 4 \, m/s^{2}$ right

C

$a_{A} = 1m / s^{2}$ towards left and $a_{B} = 1m / s^{2}$ right

D

$a_{A}=0$ and $a_{B}=4\ m/s^{2}$ right

Question 47: Palette 47/136

Allen MCQ

Statement-1: A reference frame attached to the earth is an inertial frame of reference. and Statement-2: In practical, Newton's laws can be applied in this frame of reference.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Question 48: Palette 48/136

Allen MCQ

A lift is going up. The total mass of the lift and the passengers is 500 kg. The speed of lift varies with time as shown in figure. What will be the tension (in kN) in the rope pulling the lift at t = 27s. $g = 9.8 \, m/s^{2}$

A

2

B

4

C

6

D

8

Question 49: Palette 49/136

Allen MCQ

An airplane is moving horizontally with constant acceleration $5 \, m/s^{2}$ with a block of mass $2kg$ is hanging with it, which is at rest w.r.t. plane find angle $\theta$ which string makes with vertical?

A

$\tan \theta = 2$

B

$\cot \theta = 2$

C

$\sin \theta = \frac {1}{2}$

D

$\cos \theta = \frac{1}{2}$

Question 50: Palette 50/136

Allen MCQ

If acceleration (in $m/s^{2}$ ) of wedge (rightwards) so that block does not move w.r.t. wedge is $\frac{8n}{3}$ . Value of n.

A

7

B

8

C

5

D

9

Question 51: Palette 51/136

Allen MCQ

In the figure shown, blocks A and B move with velocities $v_{1}$ and $v_{2}$ along horizontal direction. Find the ratio of $\frac{v_{1}}{v_{2}}$ .

A

$\frac{\cos\theta_1}{\cos\theta_2}$

B

$\frac{\cos\theta_2}{\cos\theta_1}$

C

$\frac{\sin\theta_2}{\sin\theta_1}$

D

$\frac{\sin\theta_1}{\sin\theta_2}$

Question 52: Palette 52/136

Allen MCQ

A block is moving along y-axis with velocity 4 m/s on a plank relative to ground and the plank is moving along x-axis with velocity 3 m/s at any instant of time. The unit vector in direction of friction force acting on block at this moment of time is.

A

$\frac{3\hat{i}+4\hat{j}}{5}$

B

$\frac{3\hat{i}-4\hat{j}}{5}$

C

$\frac{-3\hat{i}+4\hat{j}}{5}$

D

$\frac{-3\hat{i}-4\hat{j}}{5}$

Question 53: Palette 53/136

Allen MCQ

For the system of blocks and pulley shown in the figure, acceleration of block is "a" and friction force acting on 10 kg block is F then :-

A

$F = 60\ N$ , $a = 0\ m/s^2$

B

$F = 50\ N$ , $a = \frac{20}{7}\ m/s^2$

C

$F = 40\ N$ , $a = 0\ m/s^2$

D

$F = 40\ N$ , $a = \frac{20}{7}\ m/s^2$

Question 54: Palette 54/136

Allen MCQ

A block of mass 2 kg is pressed against the vertical wall of coefficient of friction $\mu = 0.2$ . The value of friction force acting on the wall is :-

A

$40\sqrt{3} N$ in upward direction

B

$40\sqrt{3} N$ in downward direction

C

$20N$ in upward direction

D

No friction force acts on the block

Question 55: Palette 55/136

Allen MCQ

A block of mass M placed on rough surface of coefficient of friction equal to 3. If F is the $(4/5)$ of the minimum force required to just move, find out the force exerted by ground on the block.

A

2.6 Mg

B

Mg

C

4Mg

D

3.4 Mg

Question 56: Palette 56/136

Allen MCQ

The coefficient of friction between the block and the horizontal surface is $\mu$ as shown in figure. The block moves towards right under action of horizontal force F (figure-a). Sometime later another force P is applied to the block making an angle $\theta$ (such that $\tan \theta = \mu$ ) with vertical as shown in (figure - b). After application of force P, the acceleration of block shall Fig. (a) Fig. (b)

A

increase

B

decrease

C

remains same

D

information insufficient for drawing inference.

Question 57: Palette 57/136

Allen MCQ

A block of mass 2kg is at rest on a rough surface, of coefficient of friction 0.5. A force F is applied on the block, variation of force is represented in the figure. Speed of the block at t = 4 sec is:

A

$2 0 m / s$

B

$1 0 m / s$

C

$5 m / s$

D

$1 5 m / s$

Question 58: Palette 58/136

Allen MCQ

Figure shows a block kept on a rough inclined plane. The maximum external force down the incline for which the block remains at rest is 2N while the maximum external force up the incline for which the block is at rest is 10 N. The coefficient of static friction $\mu$ is

A

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

B

$\frac{1}{\sqrt{6}}$

C

$\sqrt{3}$

D

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

Question 59: Palette 59/136

Allen MCQ

Block A is placed on a rough wedge B which is placed on a smooth surface. The wedge has angle of inclination of $53^{\circ}$ and is imparted a horizontal acceleration g towards right. Block A is given an initial velocity $v_{0}$ with respect to wedge. Find the coefficient of friction for which block A moves with constant velocity $v_{0}$ with respect to wedge. ( $g = 10 \, m/s^{2}$ )

A

$2 / 3$

B

$3 / 7$

C

$1 / 7$

D

$1 / 3$

Question 60: Palette 60/136

Allen MCQ

A block of mass m is at rest with respect to a rough incline kept in elevator moving up with acceleration a. Which of following statements is /are correct.

A

The contact force between block and incline is vertical.

B

The contact force between block and incline is of magnitude $m(g - a)$ .

C

The contact force between block and incline is perpendicular to the incline.

D

The contact force is of magnitude mg cos θ.

Question 61: Palette 61/136

Allen MCQ

A block rests on an inclined plane at an angle $\theta$ with horizontal and there is friction between the block and the plane. The plane is accelerated to the right. If the block remains at the same position on the plane, which of the following pictures might show the free-body diagram for the block? All observation is drawn for inertial observer (All of the vectors shown are forces).

A

B

C

D

Question 62: Palette 62/136

Allen MCQ

Base angles of triangular wedge ABC are $37^{\circ}$ and $90^{\circ}$ . A uniform rope is kept over the wedge as shown in two figures. The maximum length of string which can be hanged vertically is $x_{1}$ (fig. I) and minimum length is $x_{2}$ (fig. II) in equilibrium. If $\frac{x_{1}}{x_{2}} = 3$ , find the value of coefficient of friction between rope and wedge. Fig(i) Fig(ii)

A

0.5

B

0.4

C

0.6

D

0.8

Question 63: Palette 63/136

Allen MCQ

In the figure shown a ring of mass M and a block of mass m are in equilibrium. The string is light and pulley P does not offer any friction and coefficient of friction between pole and M is $\mu$ . The frictional force offered by the pole on M is

A

Mg directed up

B

$\mu mg$ directed up

C

$(M-m)g$ directed down

D

$\mu mg$ directed down

Question 64: Palette 64/136

Allen MCQ

In the figure shown if friction coefficient of block 1kg and 2kg with inclined plane is $\mu_{1} = 0.5$ and $\mu_{2} = 0.4$ respectively, then

A

both blocks will move together.

B

both blocks will move separately.

C

there is a non-zero contact force between two blocks.

D

none of these

Question 65: Palette 65/136

Allen MCQ

For shown situation the acceleration of block is represented by : (Here t is time in second) $(g = 10 \, ms^{-2})$ So, acceleration of block remains same.

A

B

C

D

None of these

Question 66: Palette 66/136

Allen MCQ

In the figure shown, the friction coefficient between the block of mass 1 kg and the plank of mass 2 kg is 0.4 while that between the plank and floor is 0.1. A constant force ‘F’ starts acting horizontally on the upper 1 kg block. The acceleration of plank if F = 10 N is

A

$2.5m / s^{2}$

B

3.833 m/s $^{4}$

C

0.5 m/s $^{4}$

D

$1.0m / s^{2}$

Question 67: Palette 67/136

Allen MCQ

Three blocks of equal mass M are initially at rest on smooth floor. A force is applied to the system so that the three blocks are to move together. Mark the correct option.

A

The minimum coefficient of friction required is $\frac{F}{3Mg}$ .

B

The minimum coefficient of friction required is $\frac{F}{Mg}$ .

C

The minimum coefficient of friction required is $\frac{F}{2Mg}$ .

D

The minimum coefficient of friction required is $\frac{3F}{2Mg}$ .

Question 68: Palette 68/136

Allen MSQ

Consider a block suspended from a light string as shown in the figure. Which of the following pairs of forces constitute Newton's third law pair?

A

Force with which string pulls on the ceiling and the force with which string pulls on block.

B

Force with which string pulls on the block and weight of the block.

C

Force acting on block due to the earth and force the block exerts on the earth.

D

Force with which block pulls on string and force with which the string pulls on the block.

Question 69: Palette 69/136

Allen MSQ

A horse is pulling a cart on a rough surface. If take (horse + cart) as a system, then which of the following statement(s) is/are correct?

A

Force by horse on cart is an internal force.

B

Force by ground on horse is an external force.

C

Force by cart on horse is an internal force.

D

Force by ground on cart is an external force.

Question 70: Palette 70/136

Allen MSQ

For the system shown which of the option(s) are CORRECT :

A

$N\cos \theta = mg$

B

$N = mg\cos \theta$

C

N - mg cos θ = ma

D

$mg - N \cos \theta = ma \sin \theta$

Question 71: Palette 71/136

Allen MSQ

A ball is attached from the ceiling with help of three equal taut strings each making equal angle with vertical and equal angle with each other. The ball is under three forces of pull due to the string which are along the length of strings and the force of gravity acting vertically downwards.

A

resultant of the four forces on the ball can be zero.

B

resultant of the four forces on the ball can never be zero.

C

If one string is cut and its force becomes zero, the ball can remain in equilibrium in that position.

D

If one string is cut and its force becomes zero, the ball can never be in equilibrium in that position.

Question 72: Palette 72/136

Allen MSQ

A carpenter of mass 50 kg is standing on a weighing machine placed in a lift of mass 20 kg. A light string is attached to the lift. The string passes over a smooth pulley and the other end is held by the carpenter as shown. When carpenter keeps the lift moving upward with constant velocity: $(g = 10 \, m/s^{2})$

A

the reading of weighing machine is 15 kg

B

the man applies a force of 350 N on the string

C

net force on the man is 150 N

D

Net force on the weighing machine is 150 N

Question 73: Palette 73/136

Allen MSQ

In the given figure $m_{1} = 1kg$ , $m_{2} = 2kg$ , $m_{3} = 3kg$ , F = 18 N and spring constant is 100 N/m then choose the correct options. (Assume string and spring are ideal)

A

Acceleration of $m_{1}$ is $2 \, m/s^{2}$

B

Tension in string is 2N

C

Force applied by spring on block of mass $m_{2}$ is 6N

D

Acceleration of block of mass $m_{3}$ is $4 \, m/s^{2}$

Question 74: Palette 74/136

Allen MSQ

A sleeve S of mass m starts sliding down along a smooth inclined rod through a vertical distance h from rest. Cart(C) carrying the rod is moving with constant horizontal acceleration a. If N is the normal force between sleeve and rod, $V_{S/C}$ is the speed of sleeve relative to cart on reaching the lowest point and T is the time taken to reach lowest point then :

A

$N = m$ $(g\cos \theta +a\sin \theta)$

B

$V_{S/C} = \sqrt{2h(g - a\cot\theta)}$

C

$V_{S/C} = \sqrt{2h(g - a\tan\theta)}$

D

$T = \sqrt{\frac{2h}{\sin\theta(g\cos\theta - a\sin\theta)}}$

Question 75: Palette 75/136

Allen MSQ

A ball of mass m is placed on a sledge of mass M. The sledge moves on an inclined plane A of angle of inclination $\theta$ . Inclined plane A is moving with constant horizontal acceleration ‘a’ towards left (Neglect friction everywhere)

A

Normal reaction force between m and M is $m(g \cos \theta + a \sin \theta)$

B

Normal reaction force between A and M is $(M + m)$ ( $g \cos \theta + a \sin \theta$ )

C

$a_{M / A} = a_{m / A} = (g\sin \theta -a\cos \theta)$

D

$a_{M} = a_{m} = \sin \theta \sqrt{g^{2} + a^{2}}$

Question 76: Palette 76/136

Allen MSQ

A block of m = 10 kg is kept on ground. A vertically upward force $F = (10 \ t)N$ , where t is the time in seconds starts acting on it at t = 0 as shown in figure.

A

Time at which block loose contact from the surface is 10 sec.

B

Velocity of block at t = 20 sec is 50 m/s.

C

Velocity of block at t = 20 sec is 200 m/s.

D

Displacement of block in 20 sec is $\frac{500}{3}$ m.

Question 77: Palette 77/136

Allen MSQ

System shown in the figure is released from rest. Which of the following statements is/are true? $[g = 10 \, m/s^{2}]$

A

Magnitude of acceleration of each block is $3 \, m/s^{2}$ .

B

Tension in the cord A is 6.5 N.

C

Tension in the cord B is 8 N.

D

Difference of magnitudes of tensions in both the cord is 1.5 N.

Question 78: Palette 78/136

Allen MSQ

A block A and wedge B connected through a string as shown. The wedge B is moving away from the wall with acceleration $2 \, m/s^{2}$ horizontally and acceleration of block A is vertically upwards. Then

A

Acceleration of A with respect to B is $4 \, m/s^{2}$ .

B

Acceleration of A with respect to B is $2\sqrt{3}$ m/s $^{2}$ .

C

Angle $\theta$ is $60^{\circ}$ .

D

Acceleration of A is $2\sqrt{3}$ m/s $^{2}$ .

Question 79: Palette 79/136

Allen MSQ

A block is kept on a rough surface and applied with a horizontal force as shown which is gradually increasing from zero. The coefficient of static and kinetic friction are $\frac{1}{\sqrt{3}}$ then

A

When F is less than the limiting friction, angle made by net force on the block by the surface is less than $30^{\circ}$ with vertical.

B

When the block is just about to move, the angle made by net force by the surface on the block becomes equal to $30^{\circ}$ with vertical.

C

When the block starts to accelerate, the angle made by net force by the surface on the block becomes constant and equal to $30^{\circ}$ vertical.

D

The angle made by net force with vertical on the block by the surface, depends on the mass of the block.

Question 80: Palette 80/136

Allen MSQ

A block placed on a rough horizontal surface is pushed with a force F acting horizontally on the block. The magnitude of F is increased and acceleration produced is plotted in the graph shown.

A

Mass of the block is 2 kg.

B

Coefficient of friction between block and surface is 0.5.

C

Limiting friction between block and surface is 10 N.

D

When F = 8 N, friction between block and surface is 10 N.

Question 81: Palette 81/136

Allen MSQ

A block placed on rough inclined plane is pushed with a force F. The coefficient of friction is $\mu = 0.5$ and mass of block is 10 kg.

A

If F = 30 N, acceleration of block is zero and friction acting on block is 30 N.

B

If F = 60 N, acceleration of block is zero and friction acting on block is 60 N.

C

If $F = 90N$ , acceleration of block is zero and friction acting on block is $30N$ .

D

If F = 120 N, acceleration of block is $2 \, m/s^{2}$ and friction acting on block is 40 N.

Question 82: Palette 82/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Acceleration (a) of the rope is

A

zero

B

$a = \frac{F_{A} + F_{B}}{m}$

C

$a = \frac{F_{A} - F_{B}}{m}$

D

$a = \frac{F_{B} - F_{A}}{m}$

Question 83: Palette 83/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Tension (T) at the mid point of the rope is

A

$T = F_{B} - F_{A}$

B

$T = F_{A} + F_{B}$

C

$T = \frac{1}{2}(F_{B} - F_{A})$

D

$T = \frac{1}{2}(F_{A} + F_{B})$

Question 84: Palette 84/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Expression $(T_{x})$ of tension at a point at distance $x$ from the end $A$ is

A

$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x + F_{A}$

B

$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x - F_{A}$

C

$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x + F_{B}$

D

$T_{x} = \left(\frac{F_{B} - F_{A}}{L}\right)x - F_{B}$

Question 85: Palette 85/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 63 TO 66

A uniform rope of mass $(m)$ and length $(L)$ placed on frictionless horizontal ground is being pulled by two forces $F_{A}$ and $F_{B}$ at its ends as shown in the figure. As a result, the rope accelerates toward the right. Which of the following graph best represents variation in tension at a point on the rope with distance x of the point from the end A?

A

B

C

D

Question 86: Palette 86/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 67 TO 69

A block of mass m is placed on a smooth horizontal floor is attached to one end of spring. The other end of the spring is attached to fixed support. When spring is vertical it is relaxed. Now the block is pulled towards right by a force F, which is being increased gradually. When the spring makes angle $53^{\circ}$ with the vertical, block leaves the floor. When blocks leaves the table, the normal force on it from table is

A

mg

B

zero

C

$\frac{4mg}{3}$

D

$\frac{3mg}{4}$

Question 87: Palette 87/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 67 TO 69

A block of mass m is placed on a smooth horizontal floor is attached to one end of spring. The other end of the spring is attached to fixed support. When spring is vertical it is relaxed. Now the block is pulled towards right by a force F, which is being increased gradually. When the spring makes angle $53^{\circ}$ with the vertical, block leaves the floor. Force constant of the spring is :-

A

$\frac{5mg}{2\ell}$

B

$\frac{15mg}{8\ell}$

C

$\frac{5mg}{3\ell}$

D

$\frac{5mg}{4\ell}$

Question 88: Palette 88/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 67 TO 69

A block of mass m is placed on a smooth horizontal floor is attached to one end of spring. The other end of the spring is attached to fixed support. When spring is vertical it is relaxed. Now the block is pulled towards right by a force F, which is being increased gradually. When the spring makes angle $53^{\circ}$ with the vertical, block leaves the floor. When the block leaves the table, the force F is :-

A

$\frac{3mg}{4}$

B

$\frac{4mg}{3}$

C

$\frac{3mg}{5}$

D

$\frac{4mg}{5}$

Question 89: Palette 89/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 70 TO 72

In the figure shown blocks A and B are of mass 2 kg and 8 kg and they are connected through strings to a spring connected to ground. The blocks are in equilibrium. $(g = 10m/s^{2})$ The elongation of the spring is

A

1 cm

B

10 cm

C

0.1 cm

D

1m

Question 90: Palette 90/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 70 TO 72

In the figure shown blocks A and B are of mass 2 kg and 8 kg and they are connected through strings to a spring connected to ground. The blocks are in equilibrium. $(g = 10m/s^{2})$ Now the block A is pulled downwards by a force gradually increasing to 20 N. The new elongation of spring is :-

A

2 cm

B

4 cm

C

20 cm

D

40 cm

Question 91: Palette 91/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 70 TO 72

In the figure shown blocks A and B are of mass 2 kg and 8 kg and they are connected through strings to a spring connected to ground. The blocks are in equilibrium. $(g = 10m/s^{2})$ Now the force on A is suddenly removed. The acceleration of block B becomes :-

A

1.0 m/s

B

2.0 m/s²

C

3.0 m/s²

D

4.0 m/s²

Question 92: Palette 92/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 73 TO 75

An object of mass m is suspended in equilibrium using a string of length $\ell$ and a spring having spring constant $K (< 2 \, mg/\ell)$ and unstreched length $\ell/2$ . Find the tension in the string in newton?

A

$mg - \frac{k\ell}{2}$

B

$mg - k\ell$

C

$2mg - \frac{k\ell}{2}$

D

$2mg - k\ell$

Question 93: Palette 93/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 73 TO 75

An object of mass m is suspended in equilibrium using a string of length $\ell$ and a spring having spring constant $K (< 2 \, mg/\ell)$ and unstreched length $\ell/2$ . Find the acceleration of block just after cut the string?

A

$2g - \frac{k\ell}{2m}$

B

$g - \frac{k\ell}{2m}$

C

$2g - \frac{k\ell}{m}$

D

$g - \frac{k\ell}{m}$

Question 94: Palette 94/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 73 TO 75

An object of mass m is suspended in equilibrium using a string of length $\ell$ and a spring having spring constant $K (< 2 \, mg/\ell)$ and unstreched length $\ell/2$ . What happens if $K > 2 \, mg / \ell$ ?

A

at equilibrium tension in string is negative

B

at equilibrium position change in length of spring is greater then $\frac{\ell}{2}$

C

at equilibrium tension in string is zero.

D

if cut the sting, block will accelerate in upward direction.

Question 95: Palette 95/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

When F = 2N, the frictional force between 5 kg block and ground is

A

2 N

B

0

C

8 N

D

10 N

Question 96: Palette 96/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

When $F = 2N$ , the frictional force between $10kg$ block and $5kg$ block is

A

$2N$

B

$15N$

C

$10N$

D

None

Question 97: Palette 97/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

The maximum F which will not cause motion of any of the blocks is

A

10 N

B

15 N

C

data insufficient

D

None

Question 98: Palette 98/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

The maximum acceleration of 5 kg block is :-

A

$1m / s^2$

B

$3m / s^2$

C

0

D

None

Question 99: Palette 99/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

The acceleration of 10 kg block when F = 30 N is

A

$2 \, m/s^{2}$

B

$3 \, m/s^{2}$

C

$1 \, m/s^{2}$

D

None

Question 100: Palette 100/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 76 TO 81

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

D

Question 101: Palette 101/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 82 AND 83

Given graph is a plot of magnitude of normal, limiting friction, kinetic friction and static friction versus angle of inclination $\theta$ for the coin lying on book. 17 points are labeled with numbers. The coin slips at a certain angle $\theta_{c}$ . The coefficient of static friction is 0.6, and the coefficient of kinetic friction is 0.4. The magnitude of the normal force on the coin from the book,

A

6

B

2

C

7

D

11

Question 102: Palette 102/136

Allen MCQ

Comprehension Passage: PARAGRAPH FOR QUESTION NO. 82 AND 83

Given graph is a plot of magnitude of normal, limiting friction, kinetic friction and static friction versus angle of inclination $\theta$ for the coin lying on book. 17 points are labeled with numbers. The coin slips at a certain angle $\theta_{c}$ . The coefficient of static friction is 0.6, and the coefficient of kinetic friction is 0.4. $\theta_{c}$ is given by point

A

14

B

15

C

16

D

17

Question 103: Palette 103/136

Allen MCQ

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $\theta$ as shown in figure. The coefficient of kinetic friction is $\mu_{K}$ . Then, the block's acceleration 'a' is given by: (g is acceleration due to gravity)

A

$-\frac{F}{m}\cos\theta - \mu_{K}\left(g - \frac{F}{m}\sin\theta\right)$

B

$\frac{F}{m}\cos\theta - \mu_{K}\left(g - \frac{F}{m}\sin\theta\right)$

C

$\frac{F}{m}\cos\theta - \mu_{K}\left(g + \frac{F}{m}\sin\theta\right)$

D

$\frac{F}{m}\cos\theta + \mu_{K}\left(g - \frac{F}{m}\sin\theta\right)$

Question 104: Palette 104/136

Allen 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

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 105: Palette 105/136

Allen MCQ

A block B is tied to one end of a uniform rope R as shown. The mass of block is 2 kg and that of rope is 1 kg. A force F = 15 N is applied at angle $37^{\circ}$ with vertical. The tension at the mid-point of rope is

A

$1.5N$

B

$2N$

C

$3N$

D

$4.5N$

Question 106: Palette 106/136

Allen MCQ

Same spring is attached with 2 kg, 3 kg and 1 kg blocks in three different cases as shown. If $x_{1}$ , $x_{2}$ and $x_{3}$ be the extensions in the spring in these three cases, when acceleration of both the blocks have same magnitude, then

A

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

B

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

C

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

D

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

Question 107: Palette 107/136

Allen MCQ

Three boxes are placed in a lift. When acceleration of the lift is $4 \, m/s^{2}$ , the net force on the 8 kg box is closest to

A

80 N

B

48 N

C

$40N$

D

$32N$

Question 108: Palette 108/136

Allen MCQ

Reading shown in two spring balances $S_{1}$ and $S_{2}$ is 90 kg and 30 kg respectively when lift is accelerating upwards with acceleration $10 \, m/s^{2}$ . The mass is stationary with respect to lift. Then the mass of the block will be :

A

60 kg

B

30 kg

C

120 kg

D

None of these

Question 109: Palette 109/136

Allen MCQ

On one rainy day, a sports car starts moving with a constant acceleration of $7.5 \, m/s^2$ . If a toy monkey is suspended from the ceiling of the car by a string, then at what angle the string is inclined with the vertical?

A

$37^\circ$

B

$53^\circ$

C

$45^\circ$

D

Can't be determined

Question 110: Palette 110/136

Allen MCQ

A block is placed on a rough horizontal surface. The coefficient of friction between block and surface is 0.5. A time dependent force $F = -t^2 + 6t$ is acting on the block for time $t = 0$ to $t = 6$ sec as shown in figure. Then which statement is incorrect?

A

At time t = 3 sec the friction force is maximum.

B

Block will not move in time 0 to 6 sec.

C

Maximum friction acting on block is 10 N.

D

Maximum friction acting on block is 9 N.

Question 111: Palette 111/136

Allen MCQ

A lift is going upward when suddenly cable supporting the lift breaks. From a reference frame attached to the lift, pseudo force acting on an object will have direction (After the cable broke) :-

A

Vertically downward when lift goes upward and vertically upward when lift goes downward.

B

Always vertically upward

C

Always vertically downward

D

Vertically upward when lift goes upward and vertically downward when lift goes downward.

Question 112: Palette 112/136

Allen MCQ

In the figure as shown if 2kg block is moving at an acceleration of $2m/s^{2}$ towards right, find the elongation in spring and acceleration of 4kg block at this instant. Take $g = 10\ m/s^{2}$ .

A

$0.012m, 2m / s^2$

B

$0.42\mathrm{m}, 1\mathrm{m} / \mathrm{s}^2$

C

0.012m, $1m/s^{2}$

D

0.02m, $2m/s^{2}$

Question 113: Palette 113/136

Allen MCQ

A small electrically charged sphere is suspended vertically from a thread. An oppositely charged rod is brought close to the sphere such that the sphere is in equilibrium displaced from the vertical by an angle of $30^{\circ}$ . Which one of the following best represents the free body diagram for the sphere?

A

B

C

D

Question 114: Palette 114/136

Allen MCQ

Two monkeys of masses 10 kg and 8 kg are moving along a vertical light rope, the former climbing up with an acceleration of $2 \, m/s^{2}$ , while the latter coming down with a uniform velocity of 2 m/s. Find tension in the rope at the fixed support.

A

$180N$

B

$200N$

C

$80N$

D

$216N$

Question 115: Palette 115/136

Allen MCQ

In the arrangement shown in fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed.

A

$2U\cos \theta$

B

$U\cos \theta$

C

$2U / \cos \theta$

D

$U / \cos \theta$

Question 116: Palette 116/136

Allen MCQ

As shown in figure a wedge of mass 2kg is resting on frictionless floor. A block of mass 1kg is kept on the wedge and the wedge is given an acceleration of $5 \, m/sec^{2}$ towards right. Then:

A

Block will remain stationary w.r.t wedge.

B

The block will have an acceleration of $2 \, m/sec^{2}$ w.r.t the wedge.

C

Normal reaction on the block is 8N.

D

Net force acting on the wedge is 4N.

Question 117: Palette 117/136

Allen MCQ

A block of mass 2 kg is kept on a rough horizontal floor and pulled with a force F. If the coefficient of friction is 0.5, then the minimum force required to move the block is :-

A

$10N$

B

$\frac{100}{11} N$

C

$\frac {1 0 0}{8} N$

D

$20N$

Question 118: Palette 118/136

Allen MCQ

A force $\vec{F} = \hat{i} + 4\hat{j}$ acts on block as shown. The force of friction acting on the block is :

A

$-1\hat{\imath}$

B

$-1.8\hat{\imath}$

C

$-2\hat{\imath}$

D

$-2.5\hat{\imath}$

Question 119: Palette 119/136

Allen MCQ

Block B of mass 100 kg rests on a rough surface of friction coefficient $\mu = 1/3$ . A rope is tied to block B as shown in figure. The maximum acceleration with which boy A of mass 25 kg can climbs on rope without making block move is :

A

$\frac{4g}{3}$

B

$\frac{g}{3}$

C

$\frac{g}{2}$

D

$\frac{3g}{4}$

Question 120: Palette 120/136

Allen MCQ

The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 m away from the open end, m = 0.15 kg and $g = 10 \, m/s^{2}$ . The truck starts from rest with an acceleration of $2m/s^{2}$ on a straight road. The distance moved by the truck when box falls down from the truck is:

A

4 m

B

8 m

C

16 m

D

32 m

Question 121: Palette 121/136

Allen MCQ

A block is pushed with some velocity up a rough inclined plane. It stops after ascending few meters and then reverses its direction and returns back to point from where it started. If angle of inclination is $37^{\circ}$ and the time to climb up is half of the time to return back then coefficient of friction is

A

$\frac{9}{20}$

B

$\frac{7}{5}$

C

$\frac{7}{12}$

D

$\frac{5}{7}$

Question 122: Palette 122/136

Allen 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 123: Palette 123/136

Allen MCQ

The coefficient of static and kinetic friction between the two blocks and also between the lower block and the ground are $\mu_{S} = 0.6$ and $\mu_{K} = 0.4$ . Find the value of tension T applied on the lower block at which the upper block begins to slip relative to lower block.

A

$25N$

B

$30N$

C

$40N$

D

$45N$

Question 124: Palette 124/136

Allen MCQ

The upper half of an inclined plane with inclination $\phi$ is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by -

A

$2\sin \phi$

B

$2\cos \phi$

C

$2\tan \phi$

D

$\tan \phi$

Question 125: Palette 125/136

Allen MCQ

In a given figure two masses $m_{1}$ and $m_{2}$ ( $m_{2} > m_{1}$ ) are at rest in equilibrium position. Find the tension in string AB

A

$m_{1}g$

B

$m_{2}g$

C

$(m_1 + m_2)g$

D

$(m_2 - m_1)g$

Question 126: Palette 126/136

Allen MCQ

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

A

8 N

B

10 N

C

6 N

D

4 N

Question 127: Palette 127/136

Allen MCQ

A man of mass 50 kg is pulling on a plank of mass 100 kg kept on a smooth floor as shown with force of 100 N. If both man and plank move together, find force of friction acting on man.

A

$\frac{100}{3} N$ towards left

B

$\frac{100}{3} N$ towards right

C

$\frac{250}{3} N$ towards left

D

$\frac{250}{3} N$ towards right

Question 128: Palette 128/136

Allen MCQ

In the arrangement shown in the figure, mass of the block B and A is 2m and m respectively. Surface between B and floor is smooth. The block B is connected to the block C by means of a string-pulley system. If the whole system is released, then find the minimum value of mass of block C so that A remains stationary w.r.t. B. Coefficient of friction between A and B is $\mu$ .

A

$\frac{m}{\mu}$

B

$\frac{2m + 1}{\mu + 1}$

C

$\frac{3m}{\mu - 1}$

D

$\frac{6m}{\mu + 1}$

Question 129: Palette 129/136

Allen MSQ

Refer the system shown in the figure. Block is sliding down the wedge. All surfaces are frictionless. Find correct statement(s)

A

Acceleration of block is $g \sin \theta$

B

Acceleration of block is $g \cos \theta$

C

Tension in the string is $mg \cos 2\theta$

D

Tension in the string is mg sin θ.cos θ

Question 130: Palette 130/136

Allen MSQ

The mass in the figure can slide on a frictionless surface. When the mass is pulled out, spring 1 is stretched a distance $x_{1}$ and spring 2 is stretched a distance $x_{2}$ . The spring constants are $k_{1}$ and $k_{2}$ respectively. Total magnitude of spring force pulling back on the mass is

A

$k _ {1} x _ {1}$

B

$k _ {2} x _ {2}$

C

$\left(k _ {1} x _ {1} + k _ {2} x _ {2}\right)$

D

0.5 $(k_{1} + k_{2})(x_{1} + x_{2})$

Question 131: Palette 131/136

Allen MSQ

In the given figure both the blocks have equal mass. When the thread is cut, which of the following statements give correct description immediately after the thread is cut?

A

Relative to the block A, acceleration of block B is 2g upwards.

B

Relative to the block B, acceleration of block A is 2g downwards.

C

Relative to the ground, accelerations of the blocks A and B are both g downwards.

D

Relative to the ground, accelerations of the blocks A and B are 2g downwards and zero respectively.

Question 132: Palette 132/136

Allen MSQ

A block is kept on a rough horizontal surface as shown. Its mass is 2 kg and coefficient of friction between block and surface ( $\mu$ ) = 0.5. A horizontal force F is acting on the block. When

A

F = 4 N, acceleration is zero.

B

F = 4 N, friction is 10 N and acceleration is $3 \, m/s^{2}$ .

C

F = 14 N, acceleration is $2 \, m/s^{2}$ .

D

$F = 14N$ , friction is $14N$ .

Question 133: Palette 133/136

Allen MSQ

A block of mass 1 kg is held at rest against a rough vertical surface by pushing by a force F horizontally. The coefficient of friction is 0.5. When

A

$F = 40 \, N$ , friction on the block is $20 \, N$ .

B

$F = 30 \, N$ , friction on the block is $10 \, N$ .

C

$F = 20 \, N$ , friction on the block is $10 \, N$ .

D

Minimum value of force $F$ to keep block at rest is $20 \, N$ .

Question 134: Palette 134/136

Allen MSQ

A block is released from rest from a point on a rough fixed inclined plane of inclination $37^{\circ}$ . The coefficient of friction is 0.5.

A

The time taken to slide down 9 m on the plane is 3 s.

B

The velocity of block after moving 4 m is 4 m/s.

C

The block travels equal distances in equal intervals of time.

D

The velocity of block increases linearly.

Question 135: Palette 135/136

Allen MSQ

A block is placed over a plank. The coefficient of friction between the block and the plank is $\mu = 0.2$ . Initially both are at rest, suddenly the plank starts moving with acceleration $a_0 = 4m/s^2$ . The displacement of the block in 1s is ( $g = 10m/s^2$ )

A

displacement of plank is 2 m

B

displacement of block is 1 m

C

displacement of plank is 4 m

D

displacement of block is 2 m

Question 136: Palette 136/136

Allen MSQ

Block on the sphere shown in figure is in equilibrium (it implies that net force is zero). If sphere applies a force $(N)$ of 3N on the block in the direction perpendicular to the surface of the sphere and weight of the block $(mg)$ is 5 N vertically downward. The force applied by the string on the block $(T)$ and angle $\theta$ if it acts tangentially is -

A

4

B

5

C

$37^{\circ}$

D

$53^{\circ}$