Question 1: Palette 1/268

Advance Online September 2020 MCQ

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

A

5690 J

B

5250 J

C

3280 J

D

2780 J

Question 2: Palette 2/268

Advance Online September 2020 MCQ

If the potential energy between two molecules is given by $U = -\frac{A}{r^6} + \frac{B}{r^{12}}$ , then at equilibrium, separation between molecules, and the potential energy are

A

$\left(\frac{B}{A}\right)^{\frac{1}{6}}, 0$

B

$\left(\frac{B}{2A}\right)^{\frac{1}{6}}, -\frac{A^2}{2B}$

C

$\left(\frac{2B}{A}\right)^{\frac{1}{6}}, -\frac{A^2}{4B}$

D

$\left(\frac{2B}{A}\right)^{\frac{1}{6}}, -\frac{A^2}{2B}$

Question 3: Palette 3/268

Advance Online September 2020 MCQ

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement $(s)$ time $(t)$ graph that describes the motion of the particle is (Graphs are drawn schematically and are not to scale)

A

B

C

D

Question 4: Palette 4/268

Advance Online January 2020 MCQ

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed $3 \, ms^{-1}$ . The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator ( $g = 10 \, ms^{-2}$ ) must be at least

A

56300 W

B

48000 W

C

66000 W

D

62360 W

Question 5: Palette 5/268

Advance Online January 2020 MCQ

Consider a force $\vec{F} = -x\hat{i} + y\hat{j}$ . The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment shown is .... (All quantities are in SI units)

A

$\frac{3}{2}$

B

1

C

2

D

$\frac{1}{2}$

Question 6: Palette 6/268

Advance 2020 MSQ

JEE (Advanced) 2020 A student skates up a ramp makes an angle $30^{\circ}$ with the horizontal. He/she starts (as shown in Figure) at the bottom of the ramp with speed $v_{0}$ and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in Figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

A

$v_{0}^{2}-2gh=\frac{1}{2}gR$

B

$v_{0}^{2}-2gh=\frac{\sqrt{3}}{2}gR$

C

the centripetal force required at points x and z is zero

D

the centripetal force required is maximum at points $x$ and $z$

Question 7: Palette 7/268

Advance Online April 2019 MCQ

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the Figure. The kinetic energy of the particle after it has travelled 3 m is

A

4 J

B

2.5 J

C

5 J

D

6.5 J

Question 8: Palette 8/268

Advance Online April 2019 MCQ

A uniform cable of mass M and length L is placed on a horizontal surface such that its $\left(\frac{1}{n}\right)^{\text{th}}$ part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface, the work done should be

A

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

B

nMgL

C

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

D

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

Question 9: Palette 9/268

Advance Online January 2019 MCQ

A block of mass $m$ , lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$ . The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$ , the maximum speed of the block is

A

$\frac{F}{\pi\sqrt{mk}}$

B

$\frac{\pi F}{\sqrt{mk}}$

C

$\frac{2F}{\sqrt{mk}}$

D

$\frac{F}{\sqrt{mk}}$

Question 10: Palette 10/268

Advance Online January 2019 MCQ

A force acts on a 2 kg object so that its position is given as a function of time as $x = 3t^{2} + 5$ . What is the work done by this force in first 5 seconds?

A

950 J

B

900 J

C

850 J

D

875 J

Question 11: Palette 11/268

Advance Online January 2019 MCQ

A block of mass $m$ is kept on a platform which starts from rest with constant acceleration $\frac{g}{2}$ upward, as shown in figure. Work done by normal reaction on block in time $t$ is

A

$\frac{3mg^2t^2}{8}$

B

$-\frac{mg^2t^2}{8}$

C

0

D

$\frac{mg^2t^2}{8}$

Question 12: Palette 12/268

Advance Online January 2019 MCQ

A particle which is experiencing a force, given by $\vec{F} = 3\hat{i} - 12\hat{j}$ , undergoes a displacement of $\vec{d} = 4\hat{i}$ . If the particle had a kinetic energy of $3\mathrm{J}$ at the beginning of the displacement, what is its kinetic energy of the end of the displacement?

A

15 J

B

9 J

C

12 J

D

10 J

Question 13: Palette 13/268

Advance Online January 2019 MCQ

A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_{1}$ . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_{2}$ . Then

A

$K_{2} = 2K_{1}$

B

$K_{2} = \frac{K_{1}}{4}$

C

$K_{2} = K_{1}$

D

$K_{2} = \frac{K_{1}}{2}$

Question 14: Palette 14/268

Advance 2018 MCQ

A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U = -\frac{k}{2r^2}$ . Its total energy is

A

$-\frac{k}{4a^2}$

B

$\frac{k}{2a^2}$

C

Zero

D

$-\frac{3}{2}\frac{k}{a^2}$

Question 15: Palette 15/268

Advance Online 2018 MCQ

Two particles of the same mass m are moving in circular orbits because of force, given by $F(r) = -\frac{16}{r} - r^{3}$ . The first particle is at a distance r = 1 and the second, at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to

A

$10^{-1}$

B

$6 \times 10^{-2}$

C

$6 \times 10^{2}$

D

$3 \times 10^{-3}$

Question 16: Palette 16/268

Advance Online 2018 MCQ

A body of mass m starts moving from rest along x-axis so that its velocity varies as $v = a\sqrt{s}$ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is

A

$\frac{1}{4}ma^{4}t^{2}$

B

$4ma^{4}t^{2}$

C

$\frac{1}{8}ma^{4}t^{2}$

D

$8ma^{4}t^{2}$

Question 17: Palette 17/268

Advance 2017 MCQ

A body of mass $m=10^{-2}$ kg is moving in a medium and experiences a frictional force $F=-kv^{2}$ . Its initial speed is $v_{0}=10~ms^{-1}$ . If, after 10 s, its energy is $\frac{1}{8}mv_{0}^{2}$ , the value of k will be

A

$10^{-3}$ $kgm^{-1}$

B

$10^{-3}$ $kgs^{-1}$

C

$10^{-4}$ $kgm^{-1}$

D

$10^{-1}$ $kgm^{-1}s^{-1}$

Question 18: Palette 18/268

Advance 2017 MCQ

A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 second will be

A

4.5 J

B

22 J

C

9 J

D

18 J

Question 19: Palette 19/268

Advance 2016 MCQ

A point particle having some mass, moves along the uniformly rough track $PQR$ as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu$ . The particle is released, from rest, from the point $P$ and it comes to rest at a point $R$ . The energies, lost by the ball, over the parts, $PQ$ and $QR$ , of the track, are equal to each other, and no energy is lost when particle changes direction from $PQ$ to $QR$ . The values of the coefficient of friction $\mu$ and the distance $x(= QR)$ , are respectively close to

A

0.29 and $6.5\mathrm{m}$

B

0.2 and $6.5\mathrm{m}$

C

0.2 and $3.5\mathrm{m}$

D

0.29 and $3.5\mathrm{m}$

Question 20: Palette 20/268

Advance 2016 MCQ

A person trying to lose weight by burning fat lifts a mass of 10 kg up to a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^{7}$ J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take $g = 9.8 \, ms^{-2}$

A

$12.89 \times 10^{-3} \, kg$

B

$2.45 \times 10^{-3} \, kg$

C

$6.45 \times 10^{-3} \, kg$

D

$9.89 \times 10^{-3} \, kg$

Question 21: Palette 21/268

Advance Online 2016 MCQ

Concrete mixture is made by mixing cement, stone and sand in a rotating cylinder drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to [Take the radius of the drum to be 1.25 m and its axle to be horizontal]

A

27.0

B

0.4

C

1.3

D

8.0

Question 22: Palette 22/268

Advance Online 2016 MCQ

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10 \, ms^{-1}$ , the car needs power P. If it needs power $\frac{P}{2}$ while moving downhill at speed v then value of v is

A

$20 \, ms^{-1}$

B

$5 \, ms^{-1}$

C

$15 \, ms^{-1}$

D

$10 \, ms^{-1}$

Question 23: Palette 23/268

Advance Online 2016 MCQ

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is

A

-9300 J

B

12000 J

C

-4500 J

D

-12000 J

Question 24: Palette 24/268

Advance Online 2016 MCQ

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by $n^{2}Rt^{2}$ where n is a constant. The power delivered to the particle by the force acting on it, is

A

$\frac{1}{2}Mn^{2}R^{2}t^{2}$

B

$Mn^{2}R^{2}t$

C

$MnR^{2}t^{2}$

D

$MnR^{2}t$

Question 25: Palette 25/268

Advance Online 2015 MCQ

A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance $\left(\frac{x}{2}\right)$ from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3 ms $^{-1}$ . The total initial energy of the spring is

A

1.5 J

B

0.6 J

C

0.3 J

D

0.8 J

Question 26: Palette 26/268

Advance Online 2015 MCQ

A particle is moving in a circle of radius r under the action of a force $F = \alpha r^{2}$ which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy = 0 for r = 0)

A

$\alpha r^{3}$

B

$\frac{1}{2}\alpha r^{3}$

C

$\frac{4}{3}\alpha r^{3}$

D

$\frac{5}{6}\alpha r^{3}$

Question 27: Palette 27/268

Advance 2014 MCQ

When a rubber-band is stretched by a distance $x$ , it exerts a restoring force of magnitude $F = ax + bx^2$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is

A

$aL^2 + bL^3$

B

$\frac{1}{2}(aL^2 + bL^3)$

C

$\frac{aL^2}{2} + \frac{bL^3}{3}$

D

$\frac{1}{2}\left(\frac{aL^2}{2} + \frac{bL^3}{3}\right)$

Question 28: Palette 28/268

Advance Online 2014 MCQ

A particle is released on a vertical smooth semi-circular track from point $X$ so that $OX$ makes angle $\theta$ from the vertical (see figure). The normal reaction of the track on the particle vanishes at point $Y$ where $OY$ makes angle $\phi$ with the horizontal. Then

A

$\sin \phi = \cos \phi$

B

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

C

$\sin \phi = \frac{2}{3}\cos \theta$

D

$\sin \phi = \frac{3}{4}\cos \theta$

Question 29: Palette 29/268

Advance Online 2014 MCQ

A spring of unstretched length 1 has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is

A

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

B

$mv^{2}$

C

$\frac{1}{3}mv^{2}$

D

$\frac{1}{6}mv^{2}$

Question 30: Palette 30/268

Advance Online 2014 MCQ

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be most likely proportional to

A

$v^{4}$

B

$v^{2}$

C

v

D

$v^{3}$

Question 31: Palette 31/268

Advance Online 2014 MCQ

A bullet looses $\left(\frac{1}{n}\right)^{\text {th }}$ of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be

A

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

B

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

C

Infinite

D

$n$

Question 32: Palette 32/268

Advance Online 2014 MCQ

A small ball of mass m starts at a point A with speed $v_{0}$ and moves along a frictionless track AB as shown. The track BC has coefficient of friction $\mu$ . The ball comes to stop at C after travelling a distance L which is

A

$\frac{2h}{\mu} +\frac{v_0^2}{2\mu g}$

B

$\frac{h}{\mu} +\frac{v_0^2}{2\mu g}$

C

$\frac{h}{2\mu} +\frac{v_0^2}{\mu g}$

D

$\frac{h}{2\mu} +\frac{v_0^2}{2\mu g}$

Question 33: Palette 33/268

Advance JEE (Advanced) 2014 MCQ

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

A

always radially outwards

B

always radially inwards

C

radially outwards initially and radially inwards later

D

radially inwards initially and radially outwards later

Question 34: Palette 34/268

Advance 2013 MCQ

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f\left(\frac{1}{2}mv^{2}\right)$ then $f=\left(\frac{m}{M+m}\right)$ Statement 2: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A

Statement 1 is true, Statement 2 is true, Statement-II is correct explanation of Statement-I.

B

Statement-I is true, Statement-II is true, Statement-II is not a correct explanation of Statement-I.

C

Statement-I is true, Statement-II is false.

D

Statement-I is false, Statement-II is true.

Question 35: Palette 35/268

Advance Online 2013 MCQ

A 70 kg man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force F to raise himself. The centre of gravity rises by 0.5 m before he leaps. After the leap the c.g. rises by another 1 m. The maximum power delivered by the muscles is [Take $g = 10 \, ms^{-2}$ ]

A

$6.26 \times 10^{3}$ Watts at the start

B

$6.26 \times 10^{3}$ Watts at take off

C

$6.26 \times 10^{4}$ Watts at the start

D

$6.26 \times 10^{4}$ Watts at take off

Question 36: Palette 36/268

Advance JEE (Advanced) 2013 MCQ

The work done on a particle of mass m by a force, $K\left[\frac{x}{\left(x^{2}+y^{2}\right)^{\frac{3}{2}}}\hat{i}+\frac{y}{\left(x^{2}+y^{2}\right)^{\frac{3}{2}}}\hat{j}\right]$ (K being a constant of appropriate dimensions), when the particle is taken from the point $(a,0)$ to the point $(0,a)$ along a circular path of radius a about the origin in the x-y plane is

A

$\frac{2K\pi}{a}$

B

$\frac{K\pi}{a}$

C

$\frac{K\pi}{2a}$

D

0

Question 37: Palette 37/268

Advance JEE (Advanced) 2013 MCQ

Comprehension Passage: Comprehension - 1

A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, is 150 J. (Take the acceleration due to gravity, $g = 10 \, ms^{-2}$ ) The speed of the block when it reaches the point Q is

A

$5 \, ms^{-1}$

B

$10 \, ms^{-1}$

C

$10\sqrt{3} \, ms^{-1}$

D

$20 \, ms^{-1}$

Question 38: Palette 38/268

Advance JEE (Advanced) 2013 MCQ

Comprehension Passage: Comprehension - 1

A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, is 150 J. (Take the acceleration due to gravity, $g = 10 \, ms^{-2}$ ) The magnitude of the normal reaction that acts on the block at the point Q is

A

7.5 N

B

8.6 N

C

11.5 N

D

22.5 N

Question 39: Palette 39/268

Advance 2012 MCQ

This question has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements. If two springs $S_{1}$ and $S_{2}$ of force constants $k_{1}$ and $k_{2}$ , respectively, are stretched by the same force, it is found that more work is done on spring $S_{1}$ than on spring $S_{2}$ . Statement 1: If stretched by the same amount, work done on $S_{1}$ , will be more than that on $S_{2}$ . Statement 2: $k_{1} < k_{2}$ .

A

Statement 1 is true, Statement 2 is false.

B

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

C

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

D

Statement 1 is false, Statement 2 is true.

Question 40: Palette 40/268

Advance Online 2012 MCQ

A particle gets displaced by $\Delta\bar{r}=\left(2\hat{i}+3\hat{j}+4\hat{k}\right)$ m under the action of a force $\vec{F}\left(7\hat{i}+4\hat{j}+3\hat{k}\right)$ . The change in its kinetic energy is

A

38 J

B

70 J

C

52.5 J

D

126 J

Question 41: Palette 41/268

Advance 2010 MCQ

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$ , where $a$ and b are constant and x is the distance between the atoms. If the dissociation energy of the molecule is $D=\left[U(x=\infty)-U_{\text{atequilibrium}}\right]$ , D is

A

$\frac{b^{2}}{6a}$

B

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

C

$\frac{b^{2}}{12a}$

D

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

Question 42: Palette 42/268

Advance IIT-JEE 2010 MCQ

A block of mass $2\mathrm{kg}$ is free to move along the $x$ axis. It is at rest and from $t = 0$ onwards it is subjected to a time-dependent force $F(t)$ in the $x$ direction. The force $F(t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after $4.5\mathrm{s}$ is

A

4.50 J

B

7.50 J

C

5.06 J

D

14.06 J

Question 43: Palette 43/268

Advance IIT-JEE 2008 MCQ

A block (B) is attached to two unstretched springs $S_{1}$ and $S_{2}$ with spring constants k and 4k, respectively. The other ends are attached to two supports $M_{1}$ and $M_{2}$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio $\frac{y}{x}$ is

A

4

B

2

C

$\frac{1}{2}$

D

$\frac{1}{4}$

Question 44: Palette 44/268

Advance IIT-JEE 2008 MCQ

A bob of mass M is suspended by a massless string of length L. The horizontal velocity v at position A is just sufficient to make it reach the point B. The angle $\theta$ at which the speed of the bob is half of that at A, satisfies

A

$\theta = \frac {\pi}{4}$

B

$\frac{\pi}{4} < \theta < \frac{\pi}{2}$

C

$\frac{\pi}{2}<\theta<\frac{3\pi}{4}$

D

$\frac{3\pi}{4} < \theta < \pi$

Question 45: Palette 45/268

Advance IIT-JEE 2007 MCQ

Statement-1: A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. Statement-2: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

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 46: Palette 46/268

Advance IIT-JEE 2004 MCQ

A particle is placed at the origin and a force $F = kx$ is acting on it (where $k$ is a positive constant). If $U(0) = 0$ , the graph of $U(x)$ versus $x$ will be: (where $U$ is the potential energy function)

A

B

C

D

Question 47: Palette 47/268

Advance IIT-JEE 2003 MCQ

If $W_{1}$ , $W_{2}$ and $W_{3}$ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m. Find the correct relation between $W_{1}$ , $W_{2}$ and $W_{3}$

A

$W_{1} > W_{2} > W_{3}$

B

$W_{1}=W_{2}=W_{3}$

C

$W_{1} < W_{2} < W_{3}$

D

$W_{2} > W_{1} > W_{3}$

Question 48: Palette 48/268

Advance IIT-JEE 2002 MCQ

A particle, which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as $F(x) = -kx + ax^{3}$ . Here, k and a are positive constant. For $x \geq 0$ , the functional form of the potential energy $U(x)$ of the particle is

A

B

C

$U(x)$

D

$U(x)$

Question 49: Palette 49/268

Advance 2000 MCQ

A dam is situated at a height of 550 metre above sea level and supplies water to a power house which is at a height of 50 metre above sea level. 2000 kg of water passes through the turbines per second. The maximum electrical power output of the power house if the whole system were 80% efficient is

A

8 MW

B

10 MW

C

12.5 MW

D

16 MW

Question 50: Palette 50/268

Advance IIT-JEE 2000 MCQ

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of wind energy interception by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

A

$v$

B

$v^{2}$

C

$v^{3}$

D

$v^{4}$

Question 51: Palette 51/268

Advance IIT-JEE 1999 MCQ

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of

A

$\left(\frac{2}{3}\right)k$

B

$\left(\frac{3}{2}\right)k$

C

3k

D

6k

Question 52: Palette 52/268

Advance IIT-JEE 1998 MCQ

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at the lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal is

A

$\sqrt{u^{2}-2gL}$

B

$\sqrt{2gL}$

C

$\sqrt{u^{2}-gL}$

D

$\sqrt{2(u^{2}-gL)}$

Question 53: Palette 53/268

Advance IIT-JEE 1998 MCQ

A force $\vec{F} = -k(y\hat{i} + x\hat{j})$ , where $k$ is a positive constant, acts on a particle moving in the $xy$ plane. Starting from the origin, the particle is taken along the positive $x$ -axis to the point $(a,0)$ , and then parallel to the $y$ -axis to the point $(a,a)$ . The total work done by the force on the particle is

A

$-2ka^{2}$

B

$2ka^{2}$

C

$-ka^{2}$

D

$ka^{2}$

Question 54: Palette 54/268

Advance IIT-JEE 1994 MCQ

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration $a_{c}$ is varying with time t as $a_{c}=k^{2}rt^{2}$ , where k is a constant. The power delivered to the particle by the force acting on it is

A

$2\pi mk^{2}r^{2}$

B

$mk^{2}r^{2}t$

C

$\frac{(mk^{4}r^{2}t^{5})}{3}$

D

Zero

Question 55: Palette 55/268

Advance IIT-JEE 1987 MSQ

A particle is acted upon by a force of constant magnitude which is always directed perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. From the information given, conclude that the particle

A

has constant velocity.

B

has constant acceleration.

C

has constant kinetic energy.

D

moves in a circular path.

Question 56: Palette 56/268

Advance IIT-JEE 1985 MCQ

A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. The work required to pull the hanging part on the table is

A

MgL

B

$\frac{MgL}{3}$

C

$\frac{MgL}{9}$

D

$\frac{MgL}{18}$

Question 57: Palette 57/268

Advance IIT-JEE 1984 MCQ

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

A

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

B

$t^{\frac{3}{4}}$

C

$t^{\frac{3}{2}}$

D

$t^{2}$

Question 58: Palette 58/268

Advance IIT-JEE 1980 MCQ

Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their momenta is

A

4:1

B

$\sqrt{2}$ :1

C

1:2

D

1:16

Question 59: Palette 59/268

Advance IIT-JEE 1980 MCQ

If a machine is lubricated with oil,

A

the mechanical advantage of the machine increases

B

the mechanical efficiency of the machine increases

C

both its mechanical advantage and efficiency increases

D

its efficiency increases, but its mechanical advantage decreases

Question 60: Palette 60/268

Advance 1960 MCQ

A 2 kg block is dropped from a height of 0.4 m on a spring of force constant $k = 1960 \, Nm^{-1}$ . The maximum compression of the spring is

A

0.1 m

B

0.2 m

C

0.3 m

D

0.4 m

Question 61: Palette 61/268

Advance MCQ

Two equal masses are attached to the two ends of a spring of force constant $k$ . The masses are pulled out symmetrically to stretch the spring by a length $2x_0$ over its natural length. The work done by the spring on each mass.

A

$kx_0^2$

B

$-\frac{1}{2}kx_0^2$

C

$2kx_0^2$

D

$-kx_0^2$

Question 62: Palette 62/268

Advance MCQ

An ideal spring is hung vertically from the ceiling. Spring extends by 6 cm from its natural length when 2 kg mass is attached to it. A downward external force is now applied to the mass to extend the spring slowly by an additional 10 cm. Work done by the external force is

A

-1.2 J

B

-1.8 J

C

2.4 J

D

1.6 J

Question 63: Palette 63/268

Advance MCQ

A crate of mass m falls from a height h onto the end of a platform, as shown in the figure. The spring is initially unstretched and the mass of the platform can be neglected. Assuming that there is no loss of energy, the maximum elongation of the spring is

A

$\frac{mg+\sqrt{m^{2}g^{2}+2mghk}}{k}$

B

$\frac{mg-\sqrt{m^{2}g^{2}+2mghk}}{k}$

C

$\frac{k}{\sqrt{m^{2}g^{2}+2mghk}}$

D

$\frac{\sqrt{m^{2}g^{2}+2mghk}}{k}$

Question 64: Palette 64/268

Advance MCQ

Velocity-time graph of a particle of mass 2 kg, moving in a straight line is as shown in figure. Work done by all the forces acting on the particle from t=0 to t=10 s is

A

300 J

B

-300 J

C

400 J

D

-400 J

Question 65: Palette 65/268

Advance MCQ

A particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k}$ ms $^{-1}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k}$ N. The instantaneous power applied to the particle is

A

$200$ Js $^{-1}$

B

$40$ Js $^{-1}$

C

$140$ Js $^{-1}$

D

$170$ Js $^{-1}$

Question 66: Palette 66/268

Advance MCQ

A ball suspended by a thread swings in a vertical plane so that its acceleration at the extreme position is equal to that at the lowest position. The thread deflection angle from the vertical in the extreme position is (Given: $\tan(26.5^{\circ})=0.5$ )

A

$45^{\circ}$

B

$37^{\circ}$

C

$53^{\circ}$

D

$60^{\circ}$

Question 67: Palette 67/268

Advance MCQ

A force acts on a 3 g particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^{2} + t^{3}$ , where x is in metre and t in second. The work done during the first 4 s is

A

578 mJ

B

528 mJ

C

498 mJ

D

458 mJ

Question 68: Palette 68/268

Advance MCQ

Block A of mass 45 kg is placed on a block B of mass 160 kg. Now block B is displaced by a force 50 cm horizontally towards right. During the same time block A just reaches the left end of block B as shown in Figure. Work done by frictional force on block A in ground frame during this activity is

A

-18 J

B

18 J

C

-45 J

D

45 J

Question 69: Palette 69/268

Advance MCQ

Two masses $m_{1}=10$ kg and $m_{2}=5$ kg are connected by an ideal string as shown in the figure. The coefficient of friction between $m_{1}$ and the surface is 0.2. Assuming that the system is released from rest, the velocity when $m_{2}$ has descended by 4 m is

A

$17\mathrm{ms}^{-1}$

B

$14\mathrm{ms}^{-1}$

C

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

D

$3.5\mathrm{ms}^{-1}$

Question 70: Palette 70/268

Advance MCQ

A force $\vec{F} = (2\hat{i} + 5\hat{j} + \hat{k})$ N is acting on a particle. The particle is first displaced from $(0, 0, 0)$ to $(2, 2, 0)$ m along the path $x = y$ and then from $(2, 2, 0)$ m to $(2, 2, 2)$ m along the path $x = 2$ m, $y = 2$ m. The total work done in the complete path is

A

8 J

B

10 J

C

12 J

D

16 J

Question 71: Palette 71/268

Advance MCQ

A particle is moved from $(0,0)$ to $(a,a)$ under a force $\vec{F}=\left(3\hat{i}+4\hat{j}\right)$ along two paths, Path 1 along OP and Path 2 along OQP. Let $W_{1}$ and $W_{2}$ be the work done by this force along these two paths. Then

A

$W_{1} = W_{2}$

B

$W_{1} = 2W_{2}$

C

$W_{2} = 2W_{1}$

D

$W_{2} = 4W_{1}$

Question 72: Palette 72/268

Advance MCQ

In an xy horizontal plane, a force field $\vec{F} = -(40 \text{ Nm}^{-1})(y\hat{i} + x\hat{j})$ is present where x and y are the coordinates of any point lying in the plane. A smooth rod AB is fixed in the plane as shown in the figure. A particle of mass 5 kg is to be released with a velocity in this force field such that it reaches the point B. The minimum velocity that must be imparted to the particle along the rod at A such that it reaches B is

A

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

B

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

C

$3\mathrm{ms}^{-1}$

D

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

Question 73: Palette 73/268

Advance MCQ

Work done by a force $\vec{F} = (2\hat{i} + 3\hat{j})$ N is zero, when a particle is moved along the line $3y + kx = 5$ . Then $k$ equals

A

2

B

4

C

6

D

8

Question 74: Palette 74/268

Advance MCQ

A person wants to hit a small box on the floor with a marble as shown in Figure. He compresses the spring by a distance d and releases but the marble falls short by a distance r from the box. How much should he compress the spring from natural length to land the ball in the box?

A

$\frac{d^{2}}{R-r}$

B

$\frac{d(R-r)}{R}$

C

$\frac{d(R-r)}{R+r}$

D

$\frac{Rd}{R-r}$

Question 75: Palette 75/268

Advance MCQ

An object of mass m slides down a hill of height h of arbitrary shape and after travelling a certain horizontal path stops because of friction. The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion. The work that a force must perform to return the object to its initial position along the same path is

A

mgh

B

2mgh

C

4mgh

D

-mgh

Question 76: Palette 76/268

Advance MCQ

A horizontal force in the positive direction of x-axis is applied to a 1.5 kg block initially at rest on a horizontal frictionless surface. The force is given by $\vec{F}=(4-x^{2})\hat{i}\mathrm{~N}$ , where x is in metre and the initial position of the block is x=0. The maximum kinetic energy of the block between x=0 and x=2 m is

A

2.33 J

B

8.67 J

C

5.33 J

D

6.67 J

Question 77: Palette 77/268

Advance MCQ

In the maximum positive displacement $x$ is

A

$2\sqrt{3}\mathrm{m}$

B

$2\mathrm{m}$

C

$4\mathrm{m}$

D

$\sqrt{2}\mathrm{m}$

Question 78: Palette 78/268

Advance MCQ

A particle is given an initial speed $u$ inside a smooth spherical shell so that it is just able to complete the circle. Acceleration of the particle, when its velocity is vertical will be

A

$3g$

B

$g$

C

$\sqrt{10} g$

D

$\sqrt{6} g$

Question 79: Palette 79/268

Advance MCQ

The work done in moving a particle from a point (1, 1) to (2, 3) in a plane and in a force field with potential $u = \lambda(x + y)$ is

A

3λ

B

-3λ

C

0

D

λ

Question 80: Palette 80/268

Advance MCQ

A 1.0 kg block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as shown in the figure. The work done by the force as it moves from the origin to a point x = 10 m is

A

5 J

B

30 J

C

-10 J

D

22 J

Question 81: Palette 81/268

Advance MCQ

A block of mass m is attached with a spring in its natural length, of spring constant k. The other end A of spring is moved with a constant acceleration a away from the block as shown in the figure. The maximum extension in the spring is (Assume that initially block and spring both are at rest w.r.t. ground frame)

A

$\frac{ma}{k}$

B

$\frac{1}{2}\frac{ma}{k}$

C

$\frac{2ma}{k}$

D

$\frac{4ma}{k}$

Question 82: Palette 82/268

Advance MCQ

A particle moves in the $x-y$ plane with velocity $\vec{v}=\alpha\hat{i}+\beta t\hat{j}$ . The magnitude of tangential, normal and total accelerations at $t=\frac{\alpha\sqrt{3}}{\beta}$ are

A

$\frac{\sqrt{3}}{2}\beta,\frac{\beta}{2}$ and $\beta$ respectively

B

$\frac{\beta}{2},\frac{\beta}{2}$ and $\beta$ respectively

C

$\sqrt{2}\beta,\sqrt{2}\beta$ and $\beta$ respectively

D

None of the above

Question 83: Palette 83/268

Advance MCQ

A body of mass 0.5 kg is taken up an inclined plane of length 10 m and height 5 m and then allowed to slide down to the bottom again. The coefficient of friction between the body and the plane is 0.1. The work done by the frictional force over the round trip is $\left(g = 10 \, \text{ms}^{-2}\right)$

A

5 J

B

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

C

-5 J

D

$-5\sqrt{3}$ J

Question 84: Palette 84/268

Advance MCQ

In the system shown the 5 kg block is released from rest. The pulley and spring are massless and friction is absent everywhere. The force constant of spring is $40 \, Nm^{-1}$ . The speed of 5 kg block when 2 kg block leaves contact with ground is (Take $g = 10 \, ms^{-2}$ )

A

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

B

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

C

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

D

$4\sqrt{2}\mathrm{ms}^{-1}$

Question 85: Palette 85/268

Advance MCQ

In the given system, when the ball of mass m is released from position A, it swings down the dotted arc. A nail is located at a distance d below the point of suspension such that the ball just swings completely around a circle centered on the nail. Then minimum value of d possible is

A

$0.6\mathrm{L}$

B

$0.4\mathrm{L}$

C

$0.5\mathrm{L}$

D

$0.3\mathrm{L}$

Question 86: Palette 86/268

Advance MCQ

A 60 g bullet is fired through a stack of fibre board sheets 200 mm thick. If the bullet approaches the stack with a velocity of $600 \, ms^{-1}$ and emerges out with a velocity of $300 \, ms^{-1}$ , the average resistance offered to the bullet is

A

40.5 kN

B

2 kN

C

20.25 kN

D

10 kN

Question 87: Palette 87/268

Advance MCQ

A particle of mass m begins to slide down a fixed smooth sphere from the top. What is its tangential acceleration when it leaves contact with the sphere?

A

$\frac{2g}{3}$

B

$\frac{\sqrt{5}}{3}g$

C

g

D

$\frac{g}{3}$

Question 88: Palette 88/268

Advance MCQ

A bob is suspended from a crane by a cable of length $l = 5 \, \text{m}$ . The crane and load are moving at a constant speed $v_0$ . The crane is stopped by an obstacle such that the bob on the cable swings out an angle of $60^\circ$ . The initial speed $v_0$ is $(g = 9.8 \, \text{ms}^{-2})$

A

$10 \, ms^{-1}$

B

$7 \, ms^{-1}$

C

$4 \, ms^{-1}$

D

$2 \, ms^{-1}$

Question 89: Palette 89/268

Advance MCQ

A chain of length $l$ and mass $m$ lies on the surface of a smooth sphere of radius $R(R > l)$ with one end tied on the top of the sphere. Then the gravitational potential energy of the chain with reference level at the centre of sphere is given by

A

$\frac{mR^2g}{l}\sin\left(\frac{l}{R}\right)$

B

$\frac{mR^2g}{l}\cos\left(\frac{l}{R}\right)$

C

$\frac{mR^2g}{l}\cot\left(\frac{R}{l}\right)$

D

$\frac{mR^2g}{l}\tan\left(\frac{R}{l}\right)$

Question 90: Palette 90/268

Advance MCQ

A particle of mass m attached to a string of length l is describing circular motion on a smooth plane inclined that makes an angle $\alpha$ with the horizontal. For the particle to reach the highest point its minimum velocity at the lowest point should be

A

$\sqrt{5gl}$

B

$\sqrt{5gl(\cos\alpha+1)}$

C

$\sqrt{5gl\tan\alpha}$

D

$\sqrt{5gl\sin\alpha}$

Question 91: Palette 91/268

Advance MCQ

A block is attached to a spring of stiffness k. The other end of the spring is attached to a fixed wall. The entire system lie on a horizontal surface and the spring is in natural state. The natural length of the spring is $l_{0}$ . If the block is slowly lifted up vertically to a height $\frac{5}{12}l_{0}$ from its initial position. The work done by the

A

lifting force is $\frac{kl_{0}^{2}}{288}+\frac{5}{12}mgl_{0}$

B

lifting force is $-\frac{5}{12}mgl_{0}+\frac{kl_{0}^{2}}{288}$

C

gravity is $\frac{5}{12}mgl_{0}$

D

spring force is $\frac{kl_{0}^{2}}{288}$

Question 92: Palette 92/268

Advance MCQ

Two particles 1 and 2 are descending on two frictionless chords OP and OQ. The ratio of the speeds of the particles 1 and 2 respectively, when they reach the circumference is

A

$\frac{1}{4}$

B

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

C

$\frac{1}{2}$

D

1

Question 93: Palette 93/268

Advance MCQ

An object of mass m is released from rest at N to move along the fixed smooth circular track of radius R as shown in figure. The ratio of magnitudes of centripetal force and normal reaction of the track on the object at the point P is

A

$\frac{2}{3}\sin \theta$

B

$\frac{2}{3}\cos \theta$

C

$\frac{2}{3}$

D

$\frac{3}{2}$

Question 94: Palette 94/268

Advance MCQ

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

A

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

B

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

C

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

D

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

Question 95: Palette 95/268

Advance MCQ

A small body $A$ starts sliding off the top of a smooth sphere of radius $a$ . The angle $\theta$ corresponding to the point $P$ at which the body breaks off the sphere is

A

$\cos^{-1}\left(\frac{h}{a}\right)$

B

$\cos^{-1}\left(\frac{2h}{a}\right)$

C

$\cos^{-1}\left(\frac{a}{h}\right)$

D

$\cos^{-1}\left(\frac{a}{2h}\right)$

Question 96: Palette 96/268

Advance MCQ

A body is displaced from $(0,0)$ to $(1,1)$ m along the path $x = y$ by a force $\vec{F} = (x^2\hat{j} +y\hat{i})\mathrm{N}$ . The work done by this force is

A

$\frac{4}{3}\mathrm{J}$

B

$\frac{5}{6}\mathrm{J}$

C

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

D

$\frac{7}{5}\mathrm{J}$

Question 97: Palette 97/268

Advance MCQ

A particle of mass m attached to an inextensible light string is moving in a vertical circle of radius r. Velocity at the highest point is $v_{0}$ and is just sufficient to complete the vertical circle. Tension in the string when it becomes horizontal is a. $\frac{3mv_{0}^{2}}{r}$ b. $\frac{9mv_{0}^{2}}{r}$ c. 3mg

A

a only

B

b only

C

Both b and c

D

Both a and c

Question 98: Palette 98/268

Advance MCQ

A body is moved from rest along a straight line by a machine delivering constant power. The ratio of displacement and velocity, $\left(\frac{s}{v}\right)$ varies with time $t$ as

A

B

C

D

Question 99: Palette 99/268

Advance MCQ

A particle suspended from a fixed point, by a light inextensible thread of length L is projected horizontally from its lowest position with velocity $\sqrt{\frac{7gL}{2}}$ . The string will slack after swinging through an angle $\theta$ , such that $\theta$ equals

A

$30^{\circ}$

B

$135^{\circ}$

C

$120^{\circ}$

D

$150^{\circ}$

Question 100: Palette 100/268

Advance MCQ

A man pulls a bucket of water from a depth of $h$ from a well. If the mass of the rope and that of bucket full of water are $m$ and $M$ respectively, the work done by the man is

A

$(M + m)gh$

B

$\left(M + \frac{m}{2}\right)gh$

C

$\left(\frac{M + m}{2}\right)gh$

D

$\left(\frac{M}{2} + m\right)gh$

Question 101: Palette 101/268

Advance MCQ

v-t graph of an object of mass 2 kg is shown. Select the incorrect statement

A

The average acceleration of the object is zero

B

The average velocity of the object is zero

C

The average force on the object is zero

D

Work done on the object in $30\mathrm{s}$ is zero

Question 102: Palette 102/268

Advance MCQ

A body of mass 2 kg, initially at rest, is acted upon simultaneously by two forces, one of 4 N and the other of 3 N, acting at right angles to each other. The kinetic energy of the body after 20 s is

A

500 J

B

1250 J

C

2500 J

D

5000 J

Question 103: Palette 103/268

Advance MCQ

Power supplied to a particle of mass 2 kg varies with time t (in second) as $P = \frac{3t^{2}}{2}$ W. If velocity of particle at t = 0 is v = 0. The velocity of particle at time t = 2 s will be

A

$1 \, ms^{-1}$

B

$2 \, ms^{-1}$

C

$2\sqrt{2} \, ms^{-1}$

D

$4 \, ms^{-1}$

Question 104: Palette 104/268

Advance MCQ

A particle of mass m is projected with velocity u at an angle $\alpha$ with horizontal. During the period when the particle descends from highest point to the position where its velocity vector makes an angle $\frac{\alpha}{2}$ with horizontal. Work done by gravity force is

A

$\frac{1}{2}mu^{2}\tan^{2}\alpha$

B

$\frac{1}{2}m^{2}\tan^{2}\frac{\alpha}{2}$

C

$\frac{1}{2}mu^{2}\cos^{2}\alpha\tan^{2}\frac{\alpha}{2}$

D

$\frac{1}{2}mu^{2}\cos^{2}\frac{\alpha}{2}\sin^{2}\alpha$

Question 105: Palette 105/268

Advance MCQ

A uniform rod of length 1 m and mass 100 g is pivoted at one end and is hanging vertically. It is displaced through $60^{\circ}$ from the vertical. The increase in its potential energy is $(g = 10 \, \text{ms}^{-2})$

A

0.25 J

B

0.5 J

C

0.75 J

D

1.0 J

Question 106: Palette 106/268

Advance MCQ

A running man has half the kinetic energy of a boy of half his mass. The man speeds up by $1.0 \, ms^{-1}$ and then has the same kinetic energy as the boy. The original speed of the boy was

A

$2.4 \, ms^{-1}$

B

$9.6 \, ms^{-1}$

C

$4.8 \, ms^{-1}$

D

$7.2 \, ms^{-1}$

Question 107: Palette 107/268

Advance MCQ

A body of mass m accelerates uniformly from rest to a velocity $v_{0}$ in time $t_{0}$ . The instantaneous power delivered to the body at any time t is

A

$\frac{mv_{0}t}{t_{0}}$

B

$\frac{mv_{0}^{2}t}{t_{0}}$

C

$\frac{mv_{0}t^{2}}{t_{0}}$

D

$\frac{mv_{0}^{2}}{t_{0}^{2}}t$

Question 108: Palette 108/268

Advance MCQ

One end of a spring of natural length h and spring constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h. Initially the spring makes an angle of $37^{\circ}$ with the vertical when the system is released from rest. The speed of the ring when the spring becomes vertical is

A

$\sqrt {\frac {k}{m}}$

B

$\frac {h}{2} \sqrt {\frac {k}{m}}$

C

$\frac {h}{3} \sqrt {\frac {k}{m}}$

D

$\frac {h}{4} \sqrt {\frac {k}{m}}$

Question 109: Palette 109/268

Advance MCQ

The force acting on a particle moving along x-axis varies with the position of the particle as shown in the figure. The particle is in stable equilibrium at

A

$x = x_{1}$

B

$x = x_{2}$

C

both $x_{1}$ and $x_{2}$

D

neither $x_{1}$ nor $x_{2}$

Question 110: Palette 110/268

Advance MCQ

Two masses $m_{1}$ and $m_{2}(m_{2}>m_{1})$ are positioned as shown in figure, $m_{1}$ being on the ground and $m_{2}$ at a height h above the ground. When $m_{2}$ is released, the speed at which it hits the ground will be

A

$\sqrt{\frac{2ghm_1}{m_2}}$

B

$\sqrt{\frac{2gh(m_1 - m_2)}{(m_1 + m_2)}}$

C

$\sqrt{\frac{2gh(m_1 + m_2)}{(m_1 - m_2)}}$

D

$\sqrt{\frac{2gh(m_2 - m_1)}{(m_1 + m_2)}}$

Question 111: Palette 111/268

Advance MCQ

A block of mass m slides down a rough inclined plane of inclination $\theta$ with horizontal with zero initial velocity. The coefficient of friction between the block and the plane is $\mu$ with $\theta > \tan^{-1}(\mu)$ . The rate of work done by the force of friction at time t is

A

$\mu mg^{2}t\sin\theta$

B

$mg^{2}t(\sin\theta-\mu\cos\theta)$

C

$\mu mg^{2}t\cos\theta(\sin\theta-\mu\cos\theta)$

D

$\mu mg^{2}t\cos\theta$

Question 112: Palette 112/268

Advance MCQ

A small block slides with velocity $v_{0}=\frac{1}{2}\sqrt{gr}$ on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point C. The angle $\theta$ in the figure is

A

$\cos^{-1}\left(\frac{4}{9}\right)$

B

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

C

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

D

None of the above

Question 113: Palette 113/268

Advance MCQ

A vertical spring of force constant $100 \, Nm^{-1}$ is attached with a hanging mass of 10 kg. Now an external force is applied slowly on the mass so that the spring is stretched by additional 2 m. The work done by the force F is (Take $g = 10 \, ms^{-2}$ )

A

200 J

B

400 J

C

450 J

D

600 J

Question 114: Palette 114/268

Advance MCQ

A child on a swing is 1 m above the ground at the lowest point and 6 m above the ground at the highest point. The horizontal speed of the child at the lowest point of the swing is approximately

A

$8 \, ms^{-1}$

B

$10 \, ms^{-1}$

C

$12 \, ms^{-1}$

D

$14 \, ms^{-1}$

Question 115: Palette 115/268

Advance MCQ

A force $F$ acting on a body depends on its displacement $x$ as $F \propto x^{-\frac{1}{3}}$ . The power delivered by $F$ will depend on displacement as

A

$x^{\frac{2}{3}}$

B

$x^{-\frac{5}{3}}$

C

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

D

$x^{0}$

Question 116: Palette 116/268

Advance MCQ

Two conservative forces $\vec{F}_1$ and $\vec{F}_2$ act on an object. The relation between $W_1$ and $W_2$ , where $W_1 = \oint (\vec{F}_1 + \vec{F}_2) \cdot d\vec{l}$ and $W_2 = \oint (\vec{F}_1 - \vec{F}_2) \cdot d\vec{l}$

A

$W_1 > W_2$

B

$W_1 = W_2 \neq 0$

C

$W_1 = W_2 = 0$

D

$W_1 < W_2$

Question 117: Palette 117/268

Advance MCQ

A smooth sphere of radius R is made to translate in a straight line with a constant acceleration whose magnitude is equal to the value of acceleration due to gravity. A particle kept on the top of the sphere is released from there with zero velocity with respect to the sphere. The speed of particle with respect to the sphere as a function of angle $\theta$ with the vertical, as it slides down is

A

$\frac{\sqrt{Rg(\sin\theta+\cos\theta)}}{2}$

B

$\sqrt{Rg(1+\cos\theta-\sin\theta)}$

C

$\sqrt{4Rg\sin\theta}$

D

$\sqrt{2Rg(1+\sin\theta-\cos\theta)}$

Question 118: Palette 118/268

Advance MCQ

A 100 kg drop hammer H is operated by a motor. It falls from a height of 9 m on thick nail N which is to be driven into the hard block. The hammer has to be lifted to height of 9 m in 12 s with constant velocity. If the efficiency of the motor is assumed to be 80%, the power required by the motor is approximately

A

0.49 kW

B

4.9 kW

C

0.94 kW

D

6 kW

Question 119: Palette 119/268

Advance MCQ

A block of mass 1 kg is attached to one end of a spring of force constant $k = 20 \, Nm^{-1}$ . The other end of the spring is attached to a fixed rigid support. This spring block system is made to oscillate on a rough horizontal surface having $\mu = 0.04$ . The initial displacement of the block from the equilibrium position is $a = 30 \, cm$ . The number of times the block passes from the mean position before coming to rest is $(g = 10 \, \text{ms}^{-2})$

A

15

B

11

C

7

D

6

Question 120: Palette 120/268

Advance MCQ

A motor has an electrical input of 30 kJ and is used to raise a 100 kg load to a height of 25 m when fitted to a crane winch. What is the efficiency of winch? $\left(g = 10 \, \text{ms}^{-2}\right)$

A

7.5%

B

75%

C

83.3%

D

0.75%

Question 121: Palette 121/268

Advance MCQ

A block of mass m is attached to the two springs in vertical plane as shown in the figure. If initially both the springs are at their natural lengths. Then velocity of the block is maximum at displacement x given as x is the displacement of the block from its initial position.

A

$x = \frac{mg}{2k}$

B

$x = \frac{mg}{k}$

C

$x = \frac{mg}{4k}$

D

$x = \frac{3mg}{2k}$

Question 122: Palette 122/268

Advance MCQ

Three similar cubical slabs each of mass m and edge b are lying on ground. Work done to arrange them one over the other is

A

1.5mgb

B

2mgb

C

3mgb

D

4mgb

Question 123: Palette 123/268

Advance MCQ

The potential energy function for the force between two atoms in a diatomic molecule can be expressed approximately as $U = \frac{a}{x^{12}} - \frac{b}{x^6}$ , where $a$ and $b$ are positive constants and $x$ is the distance between atoms. The dissociation energy (the energy needed to break up the molecule into separated atoms to infinity) is

A

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

B

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

C

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

D

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

Question 124: Palette 124/268

Advance MCQ

Two blocks of masses 10 kg and 5 kg are connected by a flexible but inextensible string over a shaft as shown in the figure. The system starts from rest with 10 kg mass moving downward. If a constant frictional force of 25 N acts at the shaft, the velocity when the 10 kg block has moved 2 m down is

A

$2.6\mathrm{ms}^{-1}$

B

$6.2\mathrm{ms}^{-1}$

C

$3.2\mathrm{ms}^{-1}$

D

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

Question 125: Palette 125/268

Advance MCQ

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{v}$ , where $K$ is a positive constant. The work done by this force in time $t$ is

A

$\frac{K}{v^2} t$

B

$2Kt$

C

$Kt$

D

$\frac{2Kt}{v^2}$

Question 126: Palette 126/268

Advance MCQ

A 2 HP pump is used to lift water to the overhead tank on the roof of a building. It has to be operated 8 hours per day and the cost of 1 unit of electricity is ₹6. The electricity bill for month of June will be

A

₹2148

B

₹2450

C

₹1580

D

₹840

Question 127: Palette 127/268

Advance MCQ

A pendulum of mass 1 kg and length 1 m is released from rest when it makes an angle of $60^{\circ}$ with the vertical. The power delivered by all the forces acting on the bob when it makes an angle of $30^{\circ}$ with the vertical is (Take $g = 10 \, ms^{-2}$ )

A

ZERO

B

13.4 watt

C

20.4 watt

D

24.6 watt

Question 128: Palette 128/268

Advance MCQ

The minimum speed $v$ with which a small ball should be pushed inside a smooth vertical tube of radius $R$ from a height $h$ such that it may reach the top of the tube is

A

$\sqrt{2g(h + 2R)}$

B

$\frac{5}{2} R$

C

$\sqrt{g(5R - 2h)}$

D

$\sqrt{2g(2R - h)}$

Question 129: Palette 129/268

Advance MCQ

Let a system of three blocks each of mass M, attached by light cords, placed on a horizontal surface move through a distance x with constant velocity. Then work done by the external force is

A

$3\mu_{k}Mgx$

B

$2\mu_{k}Mgx$

C

$\mathbf{Z}_{\mathrm{ERO}}$

D

$\frac{2}{3}\mu_kMgx$

Question 130: Palette 130/268

Advance MCQ

Two blocks of masses $m_{1}=1$ kg and $m_{2}=2$ kg are connected by a non-deformed light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. The minimum constant force F that has to be applied in horizontal direction to the block of mass $m_{1}$ in order to just shift the other block is (Take $g=10\ ms^{-2}$ )

A

8 N

B

15 N

C

10 N

D

25 N

Question 131: Palette 131/268

Advance MCQ

A man throws a brick to a height of 5 m where it reaches with a speed of $10 \, ms^{-1}$ . If he throws it such that it just reaches that required height, then the percentage of energy saved is $(g = 10 \, \text{ms}^{-2})$

A

29%

B

46%

C

38%

D

50%

Question 132: Palette 132/268

Advance MCQ

An object of mass $m$ is tied to string of length $L$ and a variable horizontal force is applied on it which starts at zero and gradually increases (it is pulled extremely slowly so that equilibrium exists at all times) until the string makes an angle $\theta$ with the vertical. Work done by the force $F$ is

A

$mgL(1 - \cos \theta)$

B

$mgL(1 - \sin \theta)$

C

$mgL$

D

$mgL(1 + \tan \theta)$

Question 133: Palette 133/268

Advance MCQ

A ball of mass m is attached to one end of a light rod of length l, the other end of which is hinged. The minimum velocity v that should be imparted to the ball downwards, so that it can complete the circle is

A

$\sqrt{gl}$

B

$\sqrt{2gl}$

C

$\sqrt{3gl}$

D

$\sqrt{5gl}$

Question 134: Palette 134/268

Advance MCQ

A simple pendulum swings with angular amplitude $\theta$ . When string is vertical, tension in it is twice the tension in extreme position. Then, $\cos \theta$ is equal to

A

$\frac{1}{3}$

B

$\frac{1}{2}$

C

$\frac{2}{3}$

D

$\frac{3}{4}$

Question 135: Palette 135/268

Advance MCQ

A particle is released from a height $H$ has at a certain instant kinetic energy twice its potential energy. The height and speed of particle at that instant are

A

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

B

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

C

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

D

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

Question 136: Palette 136/268

Advance MCQ

A uniform flexible chain of mass m and length 2l hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is

A

$\sqrt{2gl}$

B

$\sqrt{gl}$

C

$\sqrt{4gl}$

D

$\sqrt{3gl}$

Question 137: Palette 137/268

Advance MCQ

A system consists of two blocks of masses $m_{1}$ and $m_{2}$ respectively connected by a spring of force constant k. The force (F) that should be applied to the upper block for which the lower one just lifts after the force is removed is

A

$m_{1}g$

B

$\frac{m_1m_2}{m_1 + m_2} g$

C

$(m_1 + m_2)g$

D

$m_2g$

Question 138: Palette 138/268

Advance MCQ

A block of mass $2\mathrm{kg}$ is released from $A$ on the track that is one quadrant of a circle of radius $1\mathrm{m}$ . It slides down the track and reaches $B$ with a speed of $4\mathrm{ms}^{-1}$ and finally stops at $C$ at a distance of $3\mathrm{m}$ from $B$ . The work done against the force of friction is

A

10 J

B

20 J

C

2 J

D

6 J

Question 139: Palette 139/268

Advance MCQ

A particle moves on a rough horizontal ground with initial velocity $v_{0}$ such that $\frac{3}{4}\mathrm{th}$ of its kinetic energy is lost against friction in time $t_0$ . The coefficient of friction between the particle and the ground is

A

$\frac{v_0}{gt_0}$

B

$\frac{v_0}{2gt_0}$

C

$\frac{3v_0}{4gt_0}$

D

$\frac{v_0}{4gt_0}$

Question 140: Palette 140/268

Advance MCQ

A block of mass m is attached to a light spring of force constant k. The block is placed over a rough inclined surface for which the coefficient of friction is $\mu=\frac{3}{4}$ . The minimum value of M required to move the block up the plane is (Neglect mass of string and pulley and friction in pulley)

A

$\frac{3}{5}\mathrm{m}$

B

$\frac{4}{5}\mathrm{m}$

C

$2\mathrm{m}$

D

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

Question 141: Palette 141/268

Advance MCQ

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

A

$x$

B

$x^2$

C

$\ln x$

D

$e^x$

Question 142: Palette 142/268

Advance MCQ

The potential energy of a particle of mass m is given by $U = \begin{bmatrix} \frac{1}{2} kx^{2} & \text{for} & x < 0 \\ 0 & \text{for} & x \geq 0 \end{bmatrix}$ . If total mechanical energy of the particle is E. Then its speed at $x = \sqrt{\frac{2E}{k}}$ is

A

ZERO

B

$\sqrt{\frac{2E}{m}}$

C

$\sqrt{\frac{E}{m}}$

D

$\sqrt{\frac{E}{2m}}$

Question 143: Palette 143/268

Advance MCQ

A car of mass 1000 kg moves on a rough road where road friction is 10 percent of its weight and air friction 2 percent of its weight. To keep the car at a uniform speed of $36 \, kmhr^{-1}$ , the power required will be

A

112 kW

B

56 kW

C

12 kW

D

6 kW

Question 144: Palette 144/268

Advance MCQ

A particle of mass 0.5 kg is displaced from position $\vec{r}_{1}(2,3,1)$ m to $\vec{r}_{2}(4,3,2)$ m by applying a force of magnitude 30 N which is acting along $(\hat{i}+\hat{j}+\hat{k})$ . The work done by the force is

A

$10\sqrt{3}$ J

B

$30\sqrt{3}$ J

C

30 J

D

$\sqrt{15}$ J

Question 145: Palette 145/268

Advance MCQ

A stone of mass 1 kg tied to a light inextensible string of length $L = \frac{10}{3}$ m is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be $10 \, ms^{-2}$ , the speed of the stone at the highest point of the circle is

A

$20 \, ms^{-1}$

B

$10\sqrt{3} \, ms^{-1}$

C

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

D

$10 \, ms^{-1}$

Question 146: Palette 146/268

Advance MCQ

A simple pendulum consisting of a mass $M$ attached in a string of length $L$ is released from rest at an angle $\alpha$ . A pin is located at a distance $l$ below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. Assuming that after hitting the pin, the pendulum just oscillates, then the maximum angle $\theta$ which string makes with the vertical after hitting the pin is

A

$\cos^{-1}\left(\frac{L\cos\alpha+l}{L+l}\right)$

B

$\cos^{-1}\left(\frac{L\cos\alpha+l}{L-l}\right)$

C

$\cos^{-1}\left(\frac{L\cos\alpha-l}{L-l}\right)$

D

$\cos^{-1}\left(\frac{L\cos\alpha - l}{L + l}\right)$

Question 147: Palette 147/268

Advance MCQ

An agent applies force of constant magnitude $F_{0}$ always in the tangential direction as shown in the figure. Find the speed of the bob when string becomes horizontal, assuming that it is at rest at its lowest point

A

$\sqrt{\frac{l}{m} (\pi F_0 - 2mg)}$

B

$\sqrt{lg}$

C

$\sqrt{\frac{\pi F_0l}{m} - 4mg}$

D

$\sqrt{\frac{F_0l}{m}}$

Question 148: Palette 148/268

Advance MCQ

The tangential acceleration of a particle in a circular motion of radius 2 m is $a_{T} = \alpha t \, ms^{-2}$ (where $\alpha$ is a constant) Initially the particle is at rest. At 2 second from the start, total acceleration of the particle is equally inclined to both the accelerations. The value of constant $\alpha$ is

A

$\frac{1}{2} \, ms^{-3}$

B

$1 \, ms^{-3}$

C

$2 \, ms^{-3}$

D

$4 \, ms^{-3}$

Question 149: Palette 149/268

Advance MCQ

A car weighing 1000 kg is travelling on a level road with a uniform velocity of $60 \, kmh^{-1}$ . The resistance offered to the motion due to air and friction is 50 N. The work done by the car in travelling a distance of 1 km is

A

$5 \times 10^{4}$ J

B

$60 \times 10^{3}$ J

C

$60 \times 10^{6}$ J

D

3000 J

Question 150: Palette 150/268

Advance MCQ

A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position. This stretches the spring by a length d. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case?

A

d

B

2d

C

3d

D

$\frac{1}{2}d$

Question 151: Palette 151/268

Advance MCQ

A block of mass 4 kg slides on a horizontal smooth surface of a table with a speed $1.6 \, ms^{-1}$ . It comes to rest in compressing a spring lying in its path. If the spring has a force constant of $2 \, Nm^{-1}$ , the spring should be compressed by

A

0.22 m

B

1.4 m

C

2.2 m

D

0.4 m

Question 152: Palette 152/268

Advance MCQ

A block of mass 0.5 kg has an initial velocity of $10 \, ms^{-1}$ down an inclined rough plane of angle $30^{\circ}$ , the coefficient of friction between the block and inclined surface being 0.2. The velocity of the block after it travels a distance of 10 m is

A

$24\mathrm{ms}^{-1}$

B

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

C

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

D

$17\mathrm{ms}^{-1}$

Question 153: Palette 153/268

Advance MCQ

If the block in the shown arrangement is acted upon by a constant force $F$ for $t \geq 0$ , its maximum speed will be

A

$\frac{F}{\sqrt{mk}}$

B

$\frac{2F}{\sqrt{mk}}$

C

$\frac{F}{\sqrt{2mk}}$

D

$\frac{\sqrt{2}F}{\sqrt{mk}}$

Question 154: Palette 154/268

Advance MCQ

A projectile is fired from point O with an initial speed $V_{0}$ . The speed at an altitude h from the ground is

A

$\sqrt{V_0^2 + 2gh}$

B

$\sqrt{2gh}$

C

$\sqrt{V_0^2 - 2gh}$

D

$\sqrt{2gh - V_0^2}$

Question 155: Palette 155/268

Advance MCQ

A cube of mass M starts at rest from point 1 at a height 4R, where R is the radius of the circular track. The cube slides down the frictionless track and around the loop. The force which the track exerts on the cube at point 2 is

A

$3Mg$

B

$Mg$

C

$2Mg$

D

Cube will not reach the point 2

Question 156: Palette 156/268

Advance MCQ

A bead of mass 5 kg is free to slide on the horizontal rod AB. They are connected to two identical springs of natural length h ms as shown. If initially bead was at O and M is vertically below L then, velocity of bead (in $ms^{-1}$ ) at point N will be

A

5h

B

13.3h

C

8h

D

4h

Question 157: Palette 157/268

Advance MCQ

A ball of mass m is dropped from height h on a light platform fixed at the top of a vertical spring as shown in Figure. Speed of the ball will be maximum at the instant when compression x in the spring is

A

$\frac{mg}{k}$

B

$\frac{mg}{2k}$

C

$\frac{2mg}{k}$

D

ZERO

Question 158: Palette 158/268

Advance MSQ

A particle is taken from point $A$ to point $B$ under the influence of a force field. Now it is taken back from $B$ to $A$ and it is observed that the work done in taking the particle from $A$ to $B$ is not equal to the work done in taking it from $B$ to $A$ . If $W_{\mathrm{nc}}$ and $W_{\mathrm{c}}$ is the work done by non-conservative forces and conservative forces present in the system respectively, $\Delta U$ is the change in potential energy, $\Delta k$ is the change in kinetic energy, then

A

$W_{nc} - \Delta U = \Delta k$

B

$W_{c} = -\Delta U$

C

$W_{nc} + W_{c} = \Delta k$

D

$W_{nc} - \Delta U = -\Delta k$

Question 159: Palette 159/268

Advance MSQ

In the system shown in the figure the mass m moves in a circular arc of angular amplitude $60^{\circ}$ . Mass 4m is stationary. Then

A

the minimum value of coefficient of friction between the mass 4m and the surface of the table is 0.5

B

the work done by gravitational force on the block m is positive when it moves from A to B

C

the power delivered by the tension when m moves from A to B is zero

D

the kinetic energy of m in position B equals the work done by gravitational force on the block when it moves from position A to B

Question 160: Palette 160/268

Advance MSQ

An engine is pulling a train of mass m on a level track at a uniform speed v. The resistive force offered per unit mass is f.

A

Power produced by the engine is mfv.

B

The extra power developed by the engine to maintain a speed $v$ up a gradient of $h$ in $s$ is $\frac{mghv}{s}$ .

C

The frictional force exerting on the train is mf on the level track.

D

None of above is correct.

Question 161: Palette 161/268

Advance MSQ

In the pulley-block system shown in figure strings are light, the pulleys are light and smooth. The system is released from rest. At t = 0.3 s

A

work done on 2 kg block by gravity is 6 J

B

work done on 2 kg block by string is -2 J

C

work done on 1 kg block by gravity is -1.5 J

D

work done on 1 kg block by string is 2 J

Question 162: Palette 162/268

Advance MSQ

A block of mass 2 kg is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F = 40 N. The kinetic energy of the particle increases 40 J in a given interval of time. Then (Take $g = 10 \, ms^{-2}$ )

A

Tension in the string is 40 N

B

Displacement of the block in the given interval of time is 2 m.

C

Power developed by this force varies linearly with time

D

Power developed by this force varies parabolically with displacement.

Question 163: Palette 163/268

Advance MSQ

A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. A particle moves from $P_{1}$ to $P_{2}$ under the action of forces $\bar{F}_{1}$ , $\bar{F}_{2}$ and $\bar{F}_{3}$ . Force $\bar{F}_{1}$ is always toward $P_{2}$ and is always 20 N in magnitude. Force $\bar{F}_{2}$ always acts horizontally and is always 30 N in magnitude. Force $\bar{F}_{3}$ always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)

A

$\vec{F}_{1}$ is conservative in nature

B

work done by $\vec{F}_{1}$ is 120 J

C

work done by $\vec{F}_{2}$ is 180 J

D

work done by $\vec{F}_{3}$ is $45\pi J$

Question 164: Palette 164/268

Advance MSQ

A block of mass M is attached with a spring of spring constant k. The whole arrangement is placed on the frictionless surface of a vehicle as shown in figure. If the vehicle starts moving towards right with an acceleration a (there is no friction anywhere), then

A

maximum elongation in the spring is $\frac{Ma}{k}$

B

maximum elongation in the spring is $\frac{2Ma}{k}$

C

maximum compression in the spring is $\frac{2ma}{k}$

D

maximum compression in the spring is zero

Question 165: Palette 165/268

Advance MSQ

A particle is acted upon by a conservative force $\vec{F}=(7\hat{i}-6\hat{j})\mathrm{N}$ (no other force is acting on the particle). Under the influence of this force particle moves from $(0,0)$ to $(-3\mathrm{~m},4\mathrm{~m})$ then

A

work done by the force is 3 J

B

work done by the force is -45 J

C

at $(0, 0)$ speed of the particle must be zero

D

at $(0, 0)$ speed of the particle must not be zero

Question 166: Palette 166/268

Advance MSQ

Displacement time graph of a particle moving in a straight line is as shown in figure. Select the correct alternative(s)

A

Work done by all the forces in region $OA$ and $BC$ is positive.

B

Work done by all the forces in region AB is zero.

C

Work done by all the forces in region $BC$ is negative

D

Work done by all the forces in region OA is negative.

Question 167: Palette 167/268

Advance MSQ

A block initially suspended by an ideal spring of force constant $k$ is pulled down by applying a constant force $F$ and if maximum displacement of block from its initial mean position of rest is $x_0$ then

A

increase in energy stored in spring is $k x_{0}^{2}$

B

$x_{0}=\frac{3F}{2k}$

C

work done by applied force F is $Fx_{0}$

D

$x_{0}=\frac{2F}{k}$

Question 168: Palette 168/268

Advance MSQ

Power due to a force acting on a block varies with time t as shown in figure. Then angle between force acting on the block and its velocity is

A

acute at t = 1 s

B

$90^{\circ}$ at t = 3 s

C

obtuse at t = 7 s

D

change in kinetic energy from t = 0 to t = 10 s is 20 J

Question 169: Palette 169/268

Advance MSQ

A particle is moving in a conservative force field from point $A$ to point $B$ . $U_{\mathrm{A}}$ and $U_{\mathrm{B}}$ are the potential energies of the particle at points $A$ and $B$ and $W_{c}$ is the work done in the process of taking the particle from $A$ to $B$ .

A

$W_{\mathrm{c}} = U_{\mathrm{B}} - U_{\mathrm{A}}$

B

$W_{\mathrm{c}} = U_{\mathrm{A}} - U_{\mathrm{B}}$

C

$U_{\mathrm{A}} > U_{\mathrm{B}}$

D

$U_{\mathrm{B}} > U_{\mathrm{A}}$

Question 170: Palette 170/268

Advance MSQ

Out of the following statements, select the correct alternative(s)

A

Work done by static friction is always zero.

B

Work done by kinetic friction can also be positive.

C

Kinetic energy of a system cannot be increased without applying any external force on the system.

D

Work energy theorem is valid for non-inertial frames also.

Question 171: Palette 171/268

Advance MSQ

Kinetic energy of a particle is continuously increasing with time. It means

A

resultant force is always along the direction of motion

B

resultant force is always normal to the direction of motion

C

resultant force is at an angle less than $90^{\circ}$ to the direction of motion

D

its height above the ground level may be decreasing

E

power associated with resultant force is not equal to zero

Question 172: Palette 172/268

Advance MSQ

The potential energy of a particle of mass 1 kg in a conservative field is given as $U = \left(3x^{2}y^{2} + 6x\right)$ J, where x and y are measured in meter. Initially particle is at (1, 1) and at rest, then

A

initial acceleration of particle is $6\sqrt{5}$ ms $^{2}$

B

work done to slowly bring the particle to origin is 9 J

C

work done to slowly bring the particle to origin is -9 J

D

if particle is left free it moves in straight line

Question 173: Palette 173/268

Advance MSQ

A block of mass 2 kg is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F = 40 N. The kinetic energy of the particle is increased by 40 J in a given interval of time. Then $g = 10 \, \text{ms}^{-2}$

A

tension in the string is 40 N

B

displacement of the block in the given interval of time is 2 m

C

work done by gravity is -20 J

D

work done by tension is 80 J

Question 174: Palette 174/268

Advance MSQ

Displacement time graph of a particle moving in a straight line is as shown in figure. From the graph observe that the work done on the block is

A

positive from 0 to $t_{1}$

B

negative from $t_{1}$ to $t_{2}$

C

zero from $t_{2}$ to $t_{3}$

D

negative from $t_{3}$ to $t_{4}$

Question 175: Palette 175/268

Advance MSQ

A Block A is placed on a smooth horizontal surface and a particle C is suspended with the help of light rod from point B of the block as shown. Now both the block A and the particle C are given velocity $v_{0}$ towards left. The block A strikes a fixed wall and suddenly stops. Then, (The rod BC is free to rotate about B)

A

The smallest velocity $v_{0}$ for which the particle $C$ will swing in a full circle about the point $B$ is $\sqrt{4gl}$ .

B

The smallest velocity $v_{0}$ for which the particle $C$ will swing in a full circle about the point $B$ is $\sqrt{gl}$ .

C

Velocity of point C at the highest point of the circle (for the smallest value of $v_{0}$ ) is zero.

D

Velocity of point C at the highest point of the circle (for the smallest value of $v_{0}$ ) is $\sqrt{gl}$ .

Question 176: Palette 176/268

Advance MSQ

A force acting on an object does zero work, if

A

the force is always perpendicular to its acceleration

B

the object is stationary but the point of application of the force moves on the object

C

the force is always perpendicular to its velocity

D

the object moves in such a way that the point of application of the force remains fixed

Question 177: Palette 177/268

Advance MSQ

If the kinetic energy of a body is directly proportional to time $t$ , the magnitude of the force acting on the body is

A

directly proportional to $\sqrt{t}$

B

inversely proportional to $\sqrt{t}$

C

directly proportional to the speed of the body

D

inversely proportional to the speed of the body

Question 178: Palette 178/268

Advance MSQ

A small block of mass m is released from rest from position A inside a smooth hemispherical bowl of radius R as shown in figure. The incorrect statement(s) is/are

A

Acceleration of block is constant throughout

B

Acceleration of block at $A$ is $g$

C

Acceleration of block at B is 3g

D

Acceleration of block at B is 2g

Question 179: Palette 179/268

Advance MSQ

A particle of mass 5 kg moving in the x-y plane has its potential energy given by $U = (-7x + 24y)$ J, where x and y are in metre. The particle is initially at origin and has a velocity $\vec{u} = (14.4\hat{i} + 4.2\hat{j})$ ms $^{-1}$ .

A

The particle has a speed of $25\mathrm{ms}^{-1}$ at $t = 4\mathrm{s}$ .

B

The particle has an acceleration of $5 \, ms^{-2}$ .

C

The acceleration of the particle is perpendicular to its initial velocity.

D

None of the above is correct.

Question 180: Palette 180/268

Advance MSQ

A pendulum of length l is suspended on a flat car that is moving with a velocity u on the horizontal road. If the car is suddenly stopped, then, (assume bob of pendulum does not collide anywhere)

A

the maximum angle $\theta$ with the initial vertical line through which the pendulum swing is $\sin^{-1}\left[\frac{u}{2\sqrt{gl}}\right]$

B

the maximum angle $\theta$ with the initial vertical line through which the pendulum swing is $2\sin^{-1}\left[\frac{u}{2\sqrt{gl}}\right]$

C

if maximum angle is $60^{\circ}$ , l = 5 m and $g = 9.8 \, ms^{-2}$ then the initial speed of car u is $7 \, ms^{-1}$

D

if maximum angle $\theta$ is $30^{\circ}$ , $l = 5\mathrm{m}$ and $g = 9.8~\mathrm{ms}^{-2}$ , then the initial speed of car $u$ is $6\mathrm{ms}^{-1}$

Question 181: Palette 181/268

Advance MSQ

A small spherical ball is suspended through a string of length $l$ . The whole arrangement is placed in a vehicle which is moving with velocity $v$ . Now suddenly the vehicle stops and ball starts moving along a circular path. If tension in the string at the highest point is twice the weight of the ball and $v'$ be the velocity of ball at the highest point, then

A

$v = \sqrt{5gl}$

B

$v = \sqrt{7gl}$

C

$v' = \sqrt{gl}$

D

$v' = \sqrt{3gl}$

Question 182: Palette 182/268

Advance MSQ

One end of a light spring of force constant $k$ is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is $\frac{1}{2} kx^2$ . The possible case(s) may be

A

The spring was initially stretched by a distance x and finally was in its natural length.

B

The spring was initially in its natural length and finally it was compressed by a distance $x$ .

C

The spring was initially compressed by a distance $x$ and finally was in its natural length.

D

The spring was initially in its natural length and finally stretched by a distance $x$ .

Question 183: Palette 183/268

Advance MSQ

If a particle under the action of a force $F$ has potential energy $U$ then in equilibrium

A

$F = 0$ and $U = 0$

B

$F \neq 0$ and $U = 0$

C

$F = 0$ and $U\neq 0$

D

$F \neq 0$ and $U \neq 0$

Question 184: Palette 184/268

Advance MSQ

A block suspended from a spring is released when the spring is unstretched. Then, which of the following OPTIONS is/are correct?

A

Block starts oscillating simple harmonically.

B

Throughout the motion block is accelerated.

C

Maximum acceleration of block is g.

D

In the upward motion of block, spring is detached from the block at its mean position, then block will rise to a height greater than from where it was released.

Question 185: Palette 185/268

Advance MSQ

The potential energy U, in joule, of a particle of mass 1 kg moving in x-y plane varies as $U = 3x + 4y$ , where $(x, y)$ are the co-ordinates of the particle in metre. If the particle starts from rest from $(6, 4)$ at time t = 0 then

A

the particle has constant acceleration

B

the particle has zero acceleration

C

the speed of particle when it crosses the y-axis is $10 \, ms^{-1}$

D

co-ordinates of particle at t=1 s are (4.5, 2)

Question 186: Palette 186/268

Advance MSQ

A sledge moving over a smooth horizontal surface of ice at a velocity $v_{0}$ drives out on a horizontal road and comes to a halt as shown. The sledge has a length l, mass m and friction between runners and road is $\mu$ .

A

No work is done by the friction to switch the sledge from ice to the road.

B

A work of $\frac{1}{2}\mu mgl$ is done against friction while sledge switches completely on to road.

C

The distance covered by the sledge on the road is $\left(\frac{v_0^2}{2\mu g} -\frac{l}{2}\right)$ .

D

Total distance moved by the sledge before stopping is $\left(\frac{v_0^2}{2\mu g} +\frac{l}{2}\right)$ .

Question 187: Palette 187/268

Advance MSQ

A particle moves in a straight line with constant acceleration under a constant force F. Select the incorrect alternative(s)

A

power developed by this force varies linearly with time

B

power developed by this force varies parabolically with time

C

power developed by this force varies linearly with displacement

D

power developed by this force varies parabolically with displacement

Question 188: Palette 188/268

Advance MSQ

The spring is given a compression $a$ and released. The block of mass $m$ again comes to rest when the spring extends by $b$ . During this process, the work done by the spring on the block is $W$ . If $\mu$ be the coefficient of friction between the block and the surface, then

A

$W = \frac{1}{2} k (a + b)^{2}$

B

$W = \frac{1}{2} k \left( a^{2} - b^{2} \right)$

C

$\mu=\frac{k(a-b)}{2mg}$

D

$\mu=\frac{k(a+b)}{2mg}$

Question 189: Palette 189/268

Advance MSQ

One end of a light spring of force constant $k$ is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. For a possible displacement, the work done by the spring is $\frac{1}{2} kx^2$ . The possible case(s) may be

A

the spring was initially stretched by a distance x and finally was in its natural length

B

the spring was initially in its natural length and finally it was compressed by a distance $x$

C

the spring was initially compressed by a distance $x$ and finally was in its natural length

D

the spring was initially in its natural length and finally stretched by a distance x

Question 190: Palette 190/268

Advance MSQ

A ball of mass m is attached to the lower end of a light vertical spring of force constant k. The upper end of the spring is fixed. The ball is released from rest with the spring at its normal length and comes to rest again after descending through a distance x. Then select the correct statement(s).

A

$x = \frac{mg}{k}$

B

$x = \frac{2mg}{k}$

C

The ball will have no acceleration at the position where it has descended through $\frac{x}{2}$ .

D

The ball will have an upward acceleration equal to g at its lowermost position.

Question 191: Palette 191/268

Advance MSQ

The potential energy U for a force field $\vec{F}$ is such that U = -kxy, where k is a constant.

A

$\vec{F}=ky\hat{i}+kx\hat{j}$

B

$\vec{F}=kx\hat{i}+ky\hat{j}$

C

The force $\vec{F}$ is a conservative force

D

The force $\vec{F}$ is a non-conservative force.

Question 192: Palette 192/268

Advance MSQ

During projectile motion, the power due to gravitational force

A

is constant throughout

B

varies linearly with time

C

is positive for complete path

D

is negative for first half, zero at topmost point and positive for rest half

Question 193: Palette 193/268

Advance MSQ

Two blocks A and B having different kinetic energies $K_{A}$ and $K_{B}( > K_{A})$ are released on rough horizontal ground having same coefficient of friction for both the blocks. Then

A

momentum of B is greater than momentum of A

B

more work has to be done by friction to stop B

C

B will travel more distance before stopping

D

from the given data cannot compare the distances travelled by them before stopping

Question 194: Palette 194/268

Advance MSQ

Which of the following can be negative

A

kinetic energy

B

potential energy

C

mechanical energy

D

energy

Question 195: Palette 195/268

Advance MSQ

A force $F = -kx^{3}$ is acting on a block moving along x-axis. Here, k is a positive constant. Work done by this force is

A

positive in displacing the block from x = 3 to x = 1

B

positive in displacing the block from x = -1 to x = -3

C

negative in displacing the block from $x = 3$ to $x = 1$

D

negative in displacing the block from x = -1 to x = -3

Question 196: Palette 196/268

Advance MSQ

Suppose a car is modeled as a cylinder moving with a speed $v$ . If $A$ is the area of cross-section of the car and $\rho$ is the density of air then

A

power loss due to air resistance is $\frac{1}{2}A\rho v^{3}$

B

power loss due to air resistance is $A\rho v^{3}$

C

drag force is $\frac{1}{2} A\rho v^2$

D

drag force is $A\rho v^{2}$

Question 197: Palette 197/268

Advance MSQ

A block is suspended by an ideal spring of force constant $k$ . If the block is pulled down by applying constant force $F$ and if maximum displacement of block from its initial position of rest is $x_0$ then

A

Increase in energy stored in spring is $kx_0^2$

B

$x_0 = \frac{3F}{2k}$

C

$x_0 = \frac{2F}{k}$

D

Work done by applied force F is $Fx_{0}$

Question 198: Palette 198/268

Advance MCQ

Statement-1: Under the action of a force of constant magnitude, work done is path independent. Statement-2: Work done by force of gravity is path independent.

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 199: Palette 199/268

Advance MCQ

Statement-1: Two cars of unequal mass are moving with equal velocity in straight line. On applying equal resistive force on both the cars, work done to stop them are equal. Statement-2: Work done is equal to change in its kinetic energy.

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 200: Palette 200/268

Advance MCQ

Statement-1: A car and heavy truck have the same speed moving on a road. Same force is applied on both and both stop in same distance. Statement-2: Same force will cause the different retardation in the two vehicles.

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 201: Palette 201/268

Advance MCQ

Statement-1: The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at point B and C. Statement-2: The slope of y-x curve is zero at point B and C.

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 202: Palette 202/268

Advance MCQ

Statement-1: A body is connected to a string and if it just completes a circle, it must have zero velocity at the top. Statement-2: A body is projected in vertically upward direction, at the highest point the acceleration of particle is non-zero.

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 203: Palette 203/268

Advance MCQ

Statement-1: Consider the two situation shown in the figure. In first case height attained by particle above ground is same as the height attained by particle in case II. Statement-2: As planes are smooth so initial kinetic energy is converted into potential energy. Initial kinetic energy in two cases is different.

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 204: Palette 204/268

Advance MCQ

Statement-1: Power developed in a uniform circular motion is always zero. Statement-2: Work done in case of a uniform circular motion is zero.

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 205: Palette 205/268

Advance MCQ

Statement-1: A heavy weight is suspended from the spring. A person raises the weight slowly till the spring become slack. The work done by person is W. The energy stored on the stretched spring was E. The gain in gravitational potential energy is $(W + E)$ . Statement-2: Work done by the spring force is always negative.

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 206: Palette 206/268

Advance MCQ

Statement-1: A bomb at rest explodes into two fragments of different masses. The kinetic energies of the two fragments will be in inverse ratio of their masses. Statement-2: Kinetic energy of a body is inversely proportional to its momentum.

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 207: Palette 207/268

Advance MCQ

Statement-1: When a man raises himself up by pulling down on a horizontal bar as in a gymnasium, it is work done by the normal reaction from the bar that goes on to increase his potential energy. Statement-2: Normal force applied by the bar on the man is responsible for lifting the centre of mass of the man.

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 208: Palette 208/268

Advance MCQ

Comprehension Passage: Comprehension - 1

A small sphere B of mass m is released from rest in the position shown and swings freely in a vertical plane, first about O and then about the peg A after the cord comes in contact with the peg. Based on above information, answer the following questions. The tension in the cord just before it comes in contact with the peg is

A

$\frac{mg}{2}$

B

mg

C

$\frac{3mg}{2}$

D

2mg

Question 209: Palette 209/268

Advance MCQ

Comprehension Passage: Comprehension - 1

A small sphere B of mass m is released from rest in the position shown and swings freely in a vertical plane, first about O and then about the peg A after the cord comes in contact with the peg. Based on above information, answer the following questions. The tension in the cord just after it comes in contact with the peg is

A

$\frac{5mg}{2}$

B

$\frac{3mg}{2}$

C

$\frac{mg}{2}$

D

$\frac{mg}{4}$

Question 210: Palette 210/268

Advance MCQ

Comprehension Passage: Comprehension - 2

Consider the set up shown below in figure. Block A has a mass m and the block B has a mass 2m. The block A is attached to a rigid wall through a spring of spring constant k. The system is released from rest with the spring unstretched. Assume friction to be absent everywhere. Based on the above facts, answer the following questions. The maximum extension $x_{max}$ produced in spring is

A

$\frac{mg}{k}$

B

$\frac{2mg}{k}$

C

$\frac{3mg}{k}$

D

$\frac{4mg}{k}$

Question 211: Palette 211/268

Advance MCQ

Comprehension Passage: Comprehension - 2

Consider the set up shown below in figure. Block A has a mass m and the block B has a mass 2m. The block A is attached to a rigid wall through a spring of spring constant k. The system is released from rest with the spring unstretched. Assume friction to be absent everywhere. Based on the above facts, answer the following questions. The speed of the block A, when the extension in the spring is half the maximum extension is

A

$g\sqrt{\frac{m}{k}}$

B

$2g\sqrt{\frac{2m}{3k}}$

C

$g\sqrt{\frac{2m}{3k}}$

D

$2g\sqrt{\frac{m}{3k}}$

Question 212: Palette 212/268

Advance MCQ

Comprehension Passage: Comprehension - 2

Consider the set up shown below in figure. Block A has a mass m and the block B has a mass 2m. The block A is attached to a rigid wall through a spring of spring constant k. The system is released from rest with the spring unstretched. Assume friction to be absent everywhere. Based on the above facts, answer the following questions. Net acceleration of the block B, when extension in the spring is one fourth the maximum extension is

A

g

B

$\frac{g}{2}$

C

$\frac{g}{3}$

D

$\frac{g}{4}$

Question 213: Palette 213/268

Advance MCQ

Comprehension Passage: Comprehension - 3

A small disc A slides down with zero initial velocity from the top of a smooth hill of height H which also has a horizontal portion as shown in figure. Based on the above facts and figures, answer the following questions. The speed of launch of the particle as a projectile at lowest point of the hill $L$ is

A

$\sqrt{2gH}$

B

$\sqrt{2gh}$

C

$\sqrt{2g(H + h)}$

D

$\sqrt{2g(H - h)}$

Question 214: Palette 214/268

Advance MCQ

Comprehension Passage: Comprehension - 3

A small disc A slides down with zero initial velocity from the top of a smooth hill of height H which also has a horizontal portion as shown in figure. Based on the above facts and figures, answer the following questions. Time taken by the particle to go from L to G is

A

$\sqrt{\frac{2H}{g}}$

B

$\sqrt{\frac{2h}{g}}$

C

$\sqrt{\frac{2(H+h)}{g}}$

D

$\sqrt{\frac{2(H-h)}{g}}$

Question 215: Palette 215/268

Advance MCQ

Comprehension Passage: Comprehension - 3

A small disc A slides down with zero initial velocity from the top of a smooth hill of height H which also has a horizontal portion as shown in figure. Based on the above facts and figures, answer the following questions. The height of the horizontal portion $h$ to ensure the maximum distance $s$ covered by the disc is

A

$H$

B

$\frac{H}{2}$

C

$\frac{H}{3}$

D

$\frac{H}{4}$

Question 216: Palette 216/268

Advance MCQ

Comprehension Passage: Comprehension - 3

A small disc A slides down with zero initial velocity from the top of a smooth hill of height H which also has a horizontal portion as shown in figure. Based on the above facts and figures, answer the following questions. The maximum distance then covered by the disc is $s_{\max}$ . Then $s_{\max}$ equals

A

$\frac{H}{4}$

B

$\frac{H}{3}$

C

$\frac{H}{2}$

D

$H$

Question 217: Palette 217/268

Advance MCQ

Comprehension Passage: Comprehension - 4

A ball is released from point A as shown in figure. The ball leaves the track at B. All surfaces are smooth. Based on above information, answer the following questions. Let h be the maximum height from ground reached by ball after leaving track at B. Then

A

h = 6 m

B

h < 6 m

C

h > 6 m

D

speed of ball at B will change if shape of track is changed keeping $h_{A}$ and $h_{B}$ constant

Question 218: Palette 218/268

Advance MCQ

Comprehension Passage: Comprehension - 4

A ball is released from point A as shown in figure. The ball leaves the track at B. All surfaces are smooth. Based on above information, answer the following questions. If track makes an angle $30^{\circ}$ with horizontal at B then maximum height attained by ball will be

A

3 m

B

4 m

C

4.5 m

D

5 m

Question 219: Palette 219/268

Advance MCQ

Comprehension Passage: Comprehension - 5

The work done by a variable force $\vec{F}$ is measured by taking an infinitesimal length element $d\vec{l} = \hat{i} dx + \hat{j} dy + \hat{k} dz$ such that $W = \int \vec{F} \cdot \overline{d}\vec{l}$ . A particle of mass 2 kg is being acted upon by a variable force $\vec{F} = k(x^{2}y^{3}\hat{i} + x^{3}y^{2}\hat{j})$ . The particle is taken from (0, 0) to (a, a) along different paths. Based on the above facts, answer the following questions. The work done to take the particle from $(0, 0)$ to $(a, 0)$ (for k = 24) is

A

Zero

B

$4a^{6}$

C

$6a^{6}$

D

$8a^{6}$

Question 220: Palette 220/268

Advance MCQ

Comprehension Passage: Comprehension - 5

The work done by a variable force $\vec{F}$ is measured by taking an infinitesimal length element $d\vec{l} = \hat{i} dx + \hat{j} dy + \hat{k} dz$ such that $W = \int \vec{F} \cdot \overline{d}\vec{l}$ . A particle of mass 2 kg is being acted upon by a variable force $\vec{F} = k(x^{2}y^{3}\hat{i} + x^{3}y^{2}\hat{j})$ . The particle is taken from (0, 0) to (a, a) along different paths. Based on the above facts, answer the following questions. The work done to take the particle from $(a,0)$ to $(a,a)$ (for $k = 9$ ) is

A

Zero

B

$a^6$

C

$3a^{6}$

D

$5a^{6}$

Question 221: Palette 221/268

Advance MCQ

Comprehension Passage: Comprehension - 5

The work done by a variable force $\vec{F}$ is measured by taking an infinitesimal length element $d\vec{l} = \hat{i} dx + \hat{j} dy + \hat{k} dz$ such that $W = \int \vec{F} \cdot \overline{d}\vec{l}$ . A particle of mass 2 kg is being acted upon by a variable force $\vec{F} = k(x^{2}y^{3}\hat{i} + x^{3}y^{2}\hat{j})$ . The particle is taken from (0, 0) to (a, a) along different paths. Based on the above facts, answer the following questions. The work done to take the particle from $(0,0)$ to $(a,0)$ to $(a,a)$ is

A

$ka^6$

B

$\frac{ka^6}{2}$

C

$\frac{ka^6}{3}$

D

$\frac{ka^6}{4}$

Question 222: Palette 222/268

Advance MCQ

Comprehension Passage: Comprehension - 5

The work done by a variable force $\vec{F}$ is measured by taking an infinitesimal length element $d\vec{l} = \hat{i} dx + \hat{j} dy + \hat{k} dz$ such that $W = \int \vec{F} \cdot \overline{d}\vec{l}$ . A particle of mass 2 kg is being acted upon by a variable force $\vec{F} = k(x^{2}y^{3}\hat{i} + x^{3}y^{2}\hat{j})$ . The particle is taken from (0, 0) to (a, a) along different paths. Based on the above facts, answer the following questions. The force $\vec{F} = k\left(x^3 y^2\hat{i} + x^2 y^3\hat{j}\right)$ is a

A

conservative force

B

non-conservative force

C

force which is neither conservative nor non-conservative

D

None of above facts seems to be true

Question 223: Palette 223/268

Advance MCQ

Comprehension Passage: Comprehension - 6

A ball of mass 2 kg is released from the bottom of a tank filled with water up to 2 m. On reaching the top its kinetic energy is found to be 16 J. Ignoring the viscosity and taking $g = 10 \, ms^{-2}$ , answer the following questions. The work done by upthrust is $W_{1}$ and that done by gravity is $W_{2}$ , then

A

$W_{1}=32\ J,\ W_{2}=-16\ J$

B

$W_{1}=-16\ J,\ W_{2}=32\ J$

C

$W_{1}=40\ J,\ W_{2}=-24\ J$

D

$W_{1}=56\ J,\ W_{2}=-40\ J$

Question 224: Palette 224/268

Advance MCQ

Comprehension Passage: Comprehension - 6

A ball of mass 2 kg is released from the bottom of a tank filled with water up to 2 m. On reaching the top its kinetic energy is found to be 16 J. Ignoring the viscosity and taking $g = 10 \, ms^{-2}$ , answer the following questions. Density of the ball in $\frac{\mathrm{kg}}{\mathrm{m}^3}$ is

A

$\frac{5}{7} \times 10^{3}$

B

$\frac{3}{4} \times 10^{3}$

C

$\frac{2}{3} \times 10^{3}$

D

$\frac{1}{3} \times 10^{3}$

Question 225: Palette 225/268

Advance MCQ

Comprehension Passage: Comprehension - 7

The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions. For the particle, the equilibrium distance is $r_0$ . Then

A

$r_0 = \frac{A}{B}$

B

$r_0 = \frac{2A}{B}$

C

$r_0 = \frac{3A}{B}$

D

$r_0 = \frac{B}{4A}$

Question 226: Palette 226/268

Advance MCQ

Comprehension Passage: Comprehension - 7

The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions. The nature of the equilibrium

A

is stable

B

is unstable

C

is neutral

D

non-predictable, as data provided is insufficient

Question 227: Palette 227/268

Advance MCQ

Comprehension Passage: Comprehension - 7

The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions. The particle is moved from the equilibrium position to infinity. A work $W$ is done in the process. Then

A

$W = \frac{B^2}{2A}$

B

$W = \frac{B^2}{4A}$

C

$W = \frac{2B^2}{A}$

D

$W = \frac{4B^2}{A}$

Question 228: Palette 228/268

Advance MCQ

Comprehension Passage: Comprehension - 7

The radial component of a conservative force (like electrostatic or gravitational force) can be calculated from the potential energy function U, by using the formula $F = -\frac{dU}{dr}$ . Consider a particle bound to a certain point at a distance r from the centre of the force such that the potential energy of this particle varies with r as $U(r) = \frac{A}{r^{2}} - \frac{B}{r}$ where A and B are positive constants. Based on the above facts, answer the following questions. It is found that at a particular radial position, the total energy possessed by the particle is $E = -\frac{3B^{2}}{16A}$ . Assuming the motion to be purely radial, the velocity will be zero at position given by (in terms of equilibrium distance $r_{0}$ )

A

$r_{0}$

B

$\frac{r_{0}}{3}$

C

$\frac{2r_{0}}{3}$

D

$\frac{r_{0}}{5}$

Question 229: Palette 229/268

Advance MCQ

Comprehension Passage: Comprehension - 8

The system is released from rest with both the springs in unstretched positions. The mass of each block is 1 kg and force constant of each spring is $10 \, Nm^{-1}$ . Based on above information, answer the following questions. Extension of horizontal spring, in equilibrium, is

A

0.2 m

B

0.4 m

C

0.6 m

D

0.8 m

Question 230: Palette 230/268

Advance MCQ

Comprehension Passage: Comprehension - 8

The system is released from rest with both the springs in unstretched positions. The mass of each block is 1 kg and force constant of each spring is $10 \, Nm^{-1}$ . Based on above information, answer the following questions. Maximum speed of the block placed horizontally is

A

$1.26 \, ms^{-1}$

B

$1.93 \, ms^{-1}$

C

$2.21 \, ms^{-1}$

D

$3.21 \, ms^{-1}$

Question 231: Palette 231/268

Advance MCQ

Comprehension Passage: Comprehension - 9

The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ . For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions. The kinetic energy of the particle at the origin of the coordinates is

A

400 J

B

600 J

C

800 J

D

1000 J

Question 232: Palette 232/268

Advance MCQ

Comprehension Passage: Comprehension - 9

The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ . For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions. The kinetic energy of the body at $B$ , $x = 4 \mathrm{~m}$ is

A

376 J

B

576 J

C

776 J

D

824 J

Question 233: Palette 233/268

Advance MCQ

Comprehension Passage: Comprehension - 9

The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ . For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions. The kinetic energy of the body at $E$ , $x = 10 \, \mathrm{m}$ is

A

1036 J

B

836 J

C

636 J

D

436 J

Question 234: Palette 234/268

Advance MCQ

Comprehension Passage: Comprehension - 9

The kinetic energy is the capacity of the body to do work by virtue of its motion. For a body of mass m moving with a velocity v, it is mathematically defined as $KE = \frac{1}{2}mv^{2}$ . For conservative forces doing work, the kinetic energy always increases (or remains constant) and for non-conservative forces doing work, the kinetic energy decreases. A plot of force vs displacement is shown here. The conservative force is shown as positive and that due to non-conservative force is shown as negative. Consider a body of mass 4 kg having a velocity of $20 \, ms^{-1}$ at the origin of the coordinates. Based on the above facts and figures, answer the following questions. Let us assume the body to return to $O$ under the action of these forces, then the kinetic energy of the body at the origin of the coordinates will

A

again be 800 J

B

be more than 800 J

C

be less than 800 J

D

be greater or less than 800 J

Question 235: Palette 235/268

Advance MCQ

Comprehension Passage: Comprehension - 10

A bob of mass 1 kg is suspended from an inextensible string of length 1 m. When the string makes an angle of $60^{\circ}$ with the vertical, speed of the bob is $4 \, ms^{-1}$ . Based on above information, answer the following questions. Net acceleration of the bob at this instant is

A

$10.4 \, ms^{-2}$

B

$16 \, ms^{-2}$

C

$18.2 \, ms^{-2}$

D

$20.4 \, ms^{-2}$

Question 236: Palette 236/268

Advance MCQ

Comprehension Passage: Comprehension - 10

A bob of mass 1 kg is suspended from an inextensible string of length 1 m. When the string makes an angle of $60^{\circ}$ with the vertical, speed of the bob is $4 \, ms^{-1}$ . Based on above information, answer the following questions. The maximum height upto which the bob will rise with respect to the bottom most point is

A

1.3 m

B

>1.3 m

C

<1.3 m

D

>2 m

Question 237: Palette 237/268

Advance MCQ

Comprehension Passage: Comprehension - 11

A block is released from height $h(\neq0)$ on a rough track AB as shown in figure. The coefficient of friction between the block and the surface is $\mu=0.5$ and the track BC is smooth. From C onwards there is a circular smooth track of radius R=50 cm. Given $\tan\theta=\frac{3}{4}$ and $g=10~ms^{-2}$ . Based on above information, answer the following questions. For what value of $h$ block does not leave contact with any surface.

A

$h = 2.5 \, \text{m}$

B

$h \leq 2 \, \text{m}$

C

$h = 2 \, \text{m}$

D

$h \leq 1.5 \, \text{m}$

Question 238: Palette 238/268

Advance MCQ

Comprehension Passage: Comprehension - 11

A block is released from height $h(\neq0)$ on a rough track AB as shown in figure. The coefficient of friction between the block and the surface is $\mu=0.5$ and the track BC is smooth. From C onwards there is a circular smooth track of radius R=50 cm. Given $\tan\theta=\frac{3}{4}$ and $g=10~ms^{-2}$ . Based on above information, answer the following questions. If the block is placed on the above calculated height, how many times will the block cross point $C$ ?

A

Infinite number of times

B

2 times

C

4 times

D

3 times

Question 239: Palette 239/268

Advance MCQ

Comprehension Passage: Comprehension - 12

A projectile of mass m=1 kg is projected with velocity $v_{0}$ at angle $\theta$ . If $\vec{a}$ be the acceleration of the projectile $\vec{v}$ be its velocity, h be its height, K be its kinetic energy and U be its potential energy at any instant, then based on above information, answer the following questions. The magnitude of rate of change of potential energy of the projectile is numerically equal to the magnitude of

A

$\vec{a} \times \vec{v}$

B

$\vec{a} \cdot \vec{v}$

C

$|\vec{a} |\times |\vec{v} |$

D

$\frac{|\vec{a}|}{|\vec{v}|}$

Question 240: Palette 240/268

Advance MCQ

Comprehension Passage: Comprehension - 12

A projectile of mass m=1 kg is projected with velocity $v_{0}$ at angle $\theta$ . If $\vec{a}$ be the acceleration of the projectile $\vec{v}$ be its velocity, h be its height, K be its kinetic energy and U be its potential energy at any instant, then based on above information, answer the following questions. A graph is plotted between $\frac{K}{U}$ (on $y$ -axis), and $\frac{1}{h}$ (on $x$ -axis) then the graph will be

A

a straight line passing through origin

B

a straight line not passing through origin

C

a parabola passing through origin

D

a parabola not passing through origin

Question 241: Palette 241/268

Advance MCQ

Comprehension Passage: Comprehension - 13

A particle of mass 2 kg moving along x axis is being acted upon by a single conservative force denoted by $F(x)$ . The potential energy of the particle is $U(x)=20+(x-2)^{2}$ , where U is in joule and x is in metre. The velocity that the particle possesses at x=5 m is $4\ ms^{-1}$ . Based on the above facts, answer the following questions. The system possesses a mechanical energy equal to

A

25 J

B

35 J

C

45 J

D

55 J

Question 242: Palette 242/268

Advance MCQ

Comprehension Passage: Comprehension - 13

A particle of mass 2 kg moving along x axis is being acted upon by a single conservative force denoted by $F(x)$ . The potential energy of the particle is $U(x)=20+(x-2)^{2}$ , where U is in joule and x is in metre. The velocity that the particle possesses at x=5 m is $4\ ms^{-1}$ . Based on the above facts, answer the following questions. The maximum kinetic energy possessed by the particle is

A

15 J

B

25 J

C

30 J

D

35 J

Question 243: Palette 243/268

Advance MCQ

Comprehension Passage: Comprehension - 13

A particle of mass 2 kg moving along x axis is being acted upon by a single conservative force denoted by $F(x)$ . The potential energy of the particle is $U(x)=20+(x-2)^{2}$ , where U is in joule and x is in metre. The velocity that the particle possesses at x=5 m is $4\ ms^{-1}$ . Based on the above facts, answer the following questions. For what value of $x$ (say $x_0$ ) will the particle be in equilibrium?

A

$x_0 = 1 \, \text{m}$

B

$x_0 = 2 \, \text{m}$

C

$x_0 = 3 \, \text{m}$

D

$x_0 = 4 \, \text{m}$

Question 244: Palette 244/268

Advance MCQ

Comprehension Passage: Comprehension - 14

A block of mass $m = 2 \, kg$ is suspended by a spring of force constant $k = 10 \, Nm^{-1}$ . An another spring of same value of force constant is 1 m below it. Initially both the springs were unstretched. The block is released from rest. Based on above information, answer the following questions. The maximum extension in the upper spring is

A

$3.26\mathrm{m}$

B

$1.67\mathrm{m}$

C

$2.82\mathrm{m}$

D

None of these

Question 245: Palette 245/268

Advance MCQ

Comprehension Passage: Comprehension - 14

A block of mass $m = 2 \, kg$ is suspended by a spring of force constant $k = 10 \, Nm^{-1}$ . An another spring of same value of force constant is 1 m below it. Initially both the springs were unstretched. The block is released from rest. Based on above information, answer the following questions. The equilibrium position of the block from where it was released is

A

1 m

B

2 m

C

1.2 m

D

1.5 m

Question 246: Palette 246/268

Advance MCQ

Comprehension Passage: Comprehension - 15

The velocity versus displacement of a particle of mass 2 kg moving in a straight line is given by $$ v = \sqrt {9 + 4 s} $$ where v is in $ms^{-1}$ and s in metre. Based on above information, answer the following questions. Work done by all the forces acting on the particle in a time interval from t=0 to t=2 s is

A

10 J

B

20 J

C

30 J

D

40 J

Question 247: Palette 247/268

Advance MCQ

Comprehension Passage: Comprehension - 15

The velocity versus displacement of a particle of mass 2 kg moving in a straight line is given by $$ v = \sqrt {9 + 4 s} $$ where v is in $ms^{-1}$ and s in metre. Based on above information, answer the following questions. The average power is $\frac{3}{4}^{th}$ the instantaneous power at time $t_{0}$ , then

A

$t_{0}=1.5\ s$

B

$t_{0}=2\ s$

C

$t_{0}=2.5\ s$

D

$t_{0}=3\ s$

Question 248: Palette 248/268

Advance MCQ

Comprehension Passage: Comprehension - 16

A pendulum of mass m, length l has angular amplitude $\theta$ . Tension in the string at extreme position is $T_{1}$ and at bottom is $T_{2}$ . Based on above information, answer the following questions. If $T_{2} = T_{1}$ , then $\theta$ is equal to

A

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

B

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

C

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

D

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

Question 249: Palette 249/268

Advance MCQ

Comprehension Passage: Comprehension - 16

A pendulum of mass m, length l has angular amplitude $\theta$ . Tension in the string at extreme position is $T_{1}$ and at bottom is $T_{2}$ . Based on above information, answer the following questions. If maximum tension which the string can bear is twice the weight of bob, then the maximum value of $\theta$ is

A

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

B

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

C

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

D

$\frac{\pi}{3}$

Question 250: Palette 250/268

Advance MCQ

Comprehension Passage: Comprehension - 17

A small ball is given some velocity at point A towards right so that it moves on the semicircular track and does not leave contact up to the highest point B. After leaving the highest point B, it falls at the top of a building of height R and width $x(x \ll 2R)$ . (All the surfaces are frictionless). Based on above information, answer the following questions. The velocity given to the ball at point A so that it may hit the top of the building is

A

$\sqrt{gR}$

B

$\sqrt{2gR}$

C

$\sqrt{4gR}$

D

$\sqrt{6gR}$

Question 251: Palette 251/268

Advance MCQ

Comprehension Passage: Comprehension - 17

A small ball is given some velocity at point A towards right so that it moves on the semicircular track and does not leave contact up to the highest point B. After leaving the highest point B, it falls at the top of a building of height R and width $x(x \ll 2R)$ . (All the surfaces are frictionless). Based on above information, answer the following questions. If the collision of ball with the building is elastic, then the angle with the horizontal at which the ball will rebound from the top of the building is

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$90^{\circ}$

Question 252: Palette 252/268

Advance MCQ

Comprehension Passage: Comprehension - 17

A small ball is given some velocity at point A towards right so that it moves on the semicircular track and does not leave contact up to the highest point B. After leaving the highest point B, it falls at the top of a building of height R and width $x(x \ll 2R)$ . (All the surfaces are frictionless). Based on above information, answer the following questions. The horizontal distance of the ball from the foot of building where the ball strikes the horizontal ground is

A

$\sqrt{2}R$

B

$(1+\sqrt{2})R$

C

$2(1+\sqrt{2})R$

D

12R

Question 253: Palette 253/268

Advance MCQ

Comprehension Passage: Comprehension - 18

A particle of mass m is suspended vertically from a point O by an inextensible massless string of length L. A vertical line AB is at a distance $\frac{3\sqrt{3}}{8}L$ from O as shown in figure. The object is given a horizontal velocity $u=\sqrt{\frac{7gL}{2}}$ . At some point, its motion ceases to be circular and eventually the object passes through the line AB. At the instant of crossing AB, its velocity is horizontal. Based on above information, answer the following questions. The magnitude of the change in its velocity as it reaches a position, where the string is horizontal

A

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

B

$\sqrt{\frac{5gL}{2}}$

C

$\sqrt{3gL}$

D

$\sqrt{5gL}$

Question 254: Palette 254/268

Advance MCQ

Comprehension Passage: Comprehension - 18

A particle of mass m is suspended vertically from a point O by an inextensible massless string of length L. A vertical line AB is at a distance $\frac{3\sqrt{3}}{8}L$ from O as shown in figure. The object is given a horizontal velocity $u=\sqrt{\frac{7gL}{2}}$ . At some point, its motion ceases to be circular and eventually the object passes through the line AB. At the instant of crossing AB, its velocity is horizontal. Based on above information, answer the following questions. When the particle's motion ceases to be circular, the angle made by the string with the horizontal is

A

$30^{\circ}$

B

$60^{\circ}$

C

$37^{\circ}$

D

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

Question 255: Palette 255/268

Advance MCQ

Comprehension Passage: Comprehension - 18

A particle of mass m is suspended vertically from a point O by an inextensible massless string of length L. A vertical line AB is at a distance $\frac{3\sqrt{3}}{8}L$ from O as shown in figure. The object is given a horizontal velocity $u=\sqrt{\frac{7gL}{2}}$ . At some point, its motion ceases to be circular and eventually the object passes through the line AB. At the instant of crossing AB, its velocity is horizontal. Based on above information, answer the following questions. When the particle leaves the circular path its velocity vector is

A

$\sqrt{\frac{gL}{8}}\left(-\hat{i}+\sqrt{3}\hat{j}\right)$

B

$\sqrt{\frac{gL}{2}}\left(-\hat{i}+\sqrt{3}\hat{j}\right)$

C

$\sqrt{\frac{gL}{2}}\left(-\sqrt{3}\hat{i}+\hat{j}\right)$

D

$\sqrt{\frac{gL}{8}}\left(-\sqrt{3}\hat{i}+\hat{j}\right)$

Question 256: Palette 256/268

Advance MCQ

Comprehension Passage: Comprehension - 19

The Work Energy Theorem for a particle says, that the total work done on a particle equals the change in its kinetic energy. It means, to change the K.E. of a particle, have to apply some force on it and the force must do work on it. On a system of particles, the work done by external and internal forces on the system is equal to the change in K.E. of the system. Based on above information, answer the following questions. When you lift a stone from the floor and put it on top of the table slowly, there is no change in its K.E. This implies.

A

You have not done any work on the stone because had you done any work, then according to $W - E$ theorem the K.E. of the stone would have changed.

B

Work done by the force of gravity on the stone is also zero as that has also not lead to any change in K.E. of stone.

C

Gravity has done a positive work and you have done a negative work. Therefore, the total work done on the stone equals zero and hence change in K.E. equals zero

D

The net work done on the stone is zero and hence its change in K.E. is zero

Question 257: Palette 257/268

Advance MCQ

Comprehension Passage: Comprehension - 19

The Work Energy Theorem for a particle says, that the total work done on a particle equals the change in its kinetic energy. It means, to change the K.E. of a particle, have to apply some force on it and the force must do work on it. On a system of particles, the work done by external and internal forces on the system is equal to the change in K.E. of the system. Based on above information, answer the following questions. Suppose a heavy box is kept on a smooth inclined plane and is pushed up by a force $F$ parallel to the plane.

A

The work done by the force F as well as work done by the force of gravity both depend on how fast was the box moving at A and B as the box goes from A to B

B

The work done by the force of gravity alone depends on how fast was the box moving at $A$ and $B$ as the box goes from $A$ to $B$

C

The work done by the force F alone will depend on how fast was the box moving at A and B as the box goes from A to B

D

None of them depends on how fast the box was moving at $A$ and $B$ as the box goes from $A$ to $B$

Question 258: Palette 258/268

Advance MCQ

Comprehension Passage: Comprehension - 19

The Work Energy Theorem for a particle says, that the total work done on a particle equals the change in its kinetic energy. It means, to change the K.E. of a particle, have to apply some force on it and the force must do work on it. On a system of particles, the work done by external and internal forces on the system is equal to the change in K.E. of the system. Based on above information, answer the following questions. A balls is given a speed $V_{0}$ on a rough horizontal surface. The ball travels through a distance $l$ on the surface and stops.

A

The work done by $K$ -friction can be found by W.E. theorem as $-\mu mgl = 0 - \frac{1}{2} mv_0^2$ and hence work done by kinetic friction is positive

B

The work done by the kinetic friction can never be positive. Therefore, work done is either $-\mu mgl$ or $-\frac{1}{2} mv_0^2$ , only expressed in two different ways

C

In this case the work done by kinetic friction is negative and it can be expressed by either, $-\mu mgl$ or $-\frac{1}{2} mv_0^2$

D

The work done by kinetic friction is negative and is $\mu mgl$ and not $-\frac{1}{2}mv_{0}^{2}$ because $\frac{1}{2}mv_{0}^{2}$ is the change in K.E. and that is a result of work done by all the forces like gravity and normal reaction as well

Question 259: Palette 259/268

Advance MCQ

Comprehension Passage: Comprehension - 20

A block of mass m is released on a track shown in figure. The track is smooth from A to D and rough from point D onwards. Based on above information, answer the following questions. The normal force $N_{B}$ exerted by the track just after crossing point B is

A

2mg

B

3mg

C

4mg

D

5mg

Question 260: Palette 260/268

Advance MCQ

Comprehension Passage: Comprehension - 20

A block of mass m is released on a track shown in figure. The track is smooth from A to D and rough from point D onwards. Based on above information, answer the following questions. The normal force $N_{C}$ at $C$ is

A

$2mg$

B

$3mg$

C

$4mg$

D

$7mg$

Question 261: Palette 261/268

Advance MCQ

Comprehension Passage: Comprehension - 20

A block of mass m is released on a track shown in figure. The track is smooth from A to D and rough from point D onwards. Based on above information, answer the following questions. The distance travelled along the incline beyond point D where the block stops is

A

$\frac{2R}{\sqrt{3}\mu_{k}+1}$

B

$\frac{4R}{\mu_{k}+1}$

C

$\frac{4R}{\sqrt{3}\mu_{k}+1}$

D

$\frac{4R}{\sqrt{3}\mu_{k}+3}$

Question 262: Palette 262/268

Advance MCQ

Comprehension Passage: Comprehension - 21

A force $F = 50 \, \text{N}$ is applied at one end of a string, the other end of which is tied to a block of mass $10 \, \text{kg}$ . The block is free to move on a frictionless horizontal surface. Take initial instant as $\theta = 30^\circ$ and final instant as $\theta = 37^\circ$ . For the time between these two instants, answer the following questions? Take $\sin(37^\circ) = \frac{3}{5}$ . Net work done by the force $F$ on the block is

A

$\frac{20}{3}\mathrm{J}$

B

$\frac{50}{3}\mathrm{J}$

C

$\frac{100}{3}\mathrm{J}$

D

$75\mathrm{J}$

Question 263: Palette 263/268

Advance MCQ

Comprehension Passage: Comprehension - 21

A force $F = 50 \, \text{N}$ is applied at one end of a string, the other end of which is tied to a block of mass $10 \, \text{kg}$ . The block is free to move on a frictionless horizontal surface. Take initial instant as $\theta = 30^\circ$ and final instant as $\theta = 37^\circ$ . For the time between these two instants, answer the following questions? Take $\sin(37^\circ) = \frac{3}{5}$ . What is the final velocity of the block if initially it was at rest?

A

$\sqrt{5} \, ms^{-1}$

B

$\sqrt{\frac{25}{3}} \, ms^{-1}$

C

$\sqrt{\frac{20}{3}} \, ms^{-1}$

D

$5 \, ms^{-1}$

Question 264: Palette 264/268

Advance MCQ

Comprehension Passage: Comprehension - 21

A force $F = 50 \, \text{N}$ is applied at one end of a string, the other end of which is tied to a block of mass $10 \, \text{kg}$ . The block is free to move on a frictionless horizontal surface. Take initial instant as $\theta = 30^\circ$ and final instant as $\theta = 37^\circ$ . For the time between these two instants, answer the following questions? Take $\sin(37^\circ) = \frac{3}{5}$ . Find the ratio of initial acceleration to final acceleration of the block.

A

$\frac{3\sqrt{5}}{8}$

B

$\frac{5\sqrt{3}}{8}$

C

$\frac{8\sqrt{3}}{5}$

D

$\frac{8\sqrt{5}}{3}$

Question 265: Palette 265/268

Advance MCQ

Comprehension Passage: Comprehension - 22

A particle moves in x-y plane under the action of a path dependent force $F = y\hat{i} + x\hat{j}$ . The work done by the force as it moves in x-y plane can be evaluated by solving the line integral of force i.e. $\int\vec{F}\cdot d\vec{l}$ , where $d\vec{l}=dx\hat{i}+dy\hat{j}$ . The position coordinates x and y may vary according to some constraint determined by the path followed by the particle. Based on the information shared, answer the following questions. When the particle moves along a straight-line path from origin to the point $(a, a)$ , the work done by the force on the particle is

A

$a^2$

B

$2a$

C

$\frac{a^2}{2}$

D

Zero

Question 266: Palette 266/268

Advance MCQ

Comprehension Passage: Comprehension - 22

A particle moves in x-y plane under the action of a path dependent force $F = y\hat{i} + x\hat{j}$ . The work done by the force as it moves in x-y plane can be evaluated by solving the line integral of force i.e. $\int\vec{F}\cdot d\vec{l}$ , where $d\vec{l}=dx\hat{i}+dy\hat{j}$ . The position coordinates x and y may vary according to some constraint determined by the path followed by the particle. Based on the information shared, answer the following questions. When the particle moves from $(0, 0)$ to $(a, 0)$ and then from $(a, 0)$ to $(a, a)$ in straight line paths, then work done by the force on the particle is

A

$a^2$

B

$2a$

C

$\frac{a^2}{2}$

D

Zero

Question 267: Palette 267/268

Advance MSQ

Comprehension Passage: Comprehension - 22

A particle moves in x-y plane under the action of a path dependent force $F = y\hat{i} + x\hat{j}$ . The work done by the force as it moves in x-y plane can be evaluated by solving the line integral of force i.e. $\int\vec{F}\cdot d\vec{l}$ , where $d\vec{l}=dx\hat{i}+dy\hat{j}$ . The position coordinates x and y may vary according to some constraint determined by the path followed by the particle. Based on the information shared, answer the following questions. The infinitesimal work done (dW) by the given force when displaced through $d\vec{l}$ is given by $d W = \vec {F} \cdot d \vec {l} = y d x + x d y$ From this, it can be inferred that the work done by the force

A

depends only on initial and final values of $x$ and $y$

B

depends on initial and final values and on the path followed

C

is zero for any values of $x$ and $y$ .

D

is zero when object returns to original position after following any path.

Question 268: Palette 268/268

Advance MCQ

An ideal spring with spring constant $k$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The block is released with the spring initially unstretched. Then the maximum extension in the spring is

A

$\frac{4Mg}{k}$

B

$\frac{2Mg}{k}$

C

$\frac{Mg}{k}$

D

$\frac{Mg}{2k}$