Question 1: Palette 1/226

Errorless JEE (Main) Jan. 2025 MCQ

A force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\vec{s} = (\hat{i} - 2\hat{j} - \hat{k})$ . What will be the value of $b$ , if work done on the particle is zero

A

0

B

$\frac{1}{2}$

C

$\frac{1}{3}$

D

2

Question 2: Palette 2/226

Errorless JEE (Main) Jan. 2025 MCQ

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is

A

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

B

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

C

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

D

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

Question 3: Palette 3/226

Errorless JEE (Main) Jan. 2025 MCQ

A force $F = \alpha + \beta x^{2}$ acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant $\alpha = 1N$ then $\beta$ will be

A

$15 N/m^{2}$

B

$10 N/m^{2}$

C

$12 N/m^{2}$

D

$8 N/m^{2}$

Question 4: Palette 4/226

Errorless JEE (Main) Jan. 2025 MCQ

A bead of mass ‘m’ slides without friction on the wall of a vertical circular hoop of radius ‘R’ as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ‘R’. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ‘R’, would be (spring constant is ‘k’, g is acceleration due to gravity)

A

$2\sqrt{gR + \frac{kR^2}{m}}$

B

$\sqrt{2Rg + \frac{4kR^2}{m}}$

C

$\sqrt{2Rg + \frac{kR^2}{m}}$

D

$\sqrt{3Rg + \frac{kR^2}{m}}$

Question 5: Palette 5/226

Errorless JEF (Main) Jan 2025 MCQ

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In a central force field, the work done is independent of the path chosen Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below [JEE (Main) Jan. 2025]

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 6: Palette 6/226

Errorless JEE (Main) Jan. 2025 MCQ

As shown below, bob A of a pendulum having massless string of length 'R' is released from 60° to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the centre. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity)

A

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

B

$\sqrt{Rg}$

C

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

D

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

Question 7: Palette 7/226

Errorless JEE (Main) Jan. 2025 MCQ

A body of mass ‘m’ connected to a massless and unstretchable string goes in vertical circle of radius ‘R’ under gravity g. The other end of the string is fixed at the centre of circle. If velocity at top of circular path is $n\sqrt{gR}$ , where, $n \geq 1$ , then ratio of kinetic energy of the body at bottom to that at top of the circle is

A

$\frac{n}{n+4}$

B

$\frac{n+4}{n}$

C

$\frac{n^{2}}{n^{2}+4}$

D

$\frac{n^{2}+4}{n^{2}}$

Question 8: Palette 8/226

Errorless JEE (Main) Jan. 2025 MCQ

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_{A}=5m/s$ , $v_{B}=2m/s$ , $v_{C}=4m/s$ . If we wait sufficiently long for elastic collision to happen, then $v_{A}=4m/s$ , $v_{B}=2m/s$ , $v_{C}=5m/s$ will be the final velocities. Reason (R) : In an elastic collision between identical masses, two objects exchange their velocities. In the light of the above statements, choose the correct answer from the options given below

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 9: Palette 9/226

Errorless JEE (Main) Jan. 2024 MCQ

A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass $10^{-2}$ kg moving with a speed of $2 \times 10^{2}$ ms $^{-1}$ . The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use $g = 10 \, m/s^{2}$ )

A

0.30 m

B

0.20 m

C

0.35 m

D

0.40 m

Question 10: Palette 10/226

Errorless JEE (Main) Jan. 2024 MCQ

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is

A

3:5

B

5:4

C

2:5

D

4:5

Question 11: Palette 11/226

Errorless JEE (Main) Jan. 2024 MCQ

A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is

A

6

B

2

C

3

D

5

Question 12: Palette 12/226

Errorless JEE (Main) Jan. 2024 MCQ

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ( $\theta$ ) of thread deflection in the extreme position will be

A

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

B

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

C

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

D

$2\tan^{-1}\left(\frac{1}{\sqrt{5}}\right)$

Question 13: Palette 13/226

Errorless JEE (Main) Jan. 2024 MCQ

A bob of mass ‘m’ is suspended by a light string of length ‘L’. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies $\frac{(K.E.)_{A}}{(K.E.)_{B}}$ is

A

3:2

B

5:1

C

2:5

D

1:5

Question 14: Palette 14/226

Errorless JEE (Main) Jan. 2024 MCQ

The potential energy function (in J) of a particle in a region of space is given as $U = (2x^{2} + 3y^{3} + 2z)$ . Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point $P(1,2,3)m$ is

A

2

B

6

C

4

D

8

Question 15: Palette 15/226

Errorless JEE (Main) Jan. 2024 MCQ

A particle is placed at the point $A$ of a frictionless track $ABC$ as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point $B$ is (Take $g = 10m / s^2$ )

A

$20m / s$

B

$\sqrt{10} m / s$

C

$2\sqrt{10} m / s$

D

$10m / s$

Question 16: Palette 16/226

Errorless JEE (Main) Jan. 2024 MCQ

An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is

A

$M_{1}/(M_{1}+M_{2})$

B

$\frac{M_{2}}{M_{1}}$

C

$M_{2}/(M_{1}+M_{2})$

D

$\frac{M_{1}}{M_{2}}$

Question 17: Palette 17/226

Errorless JEE (Main) Jan. 2024 MCQ

A body of mass 2 kg begins to move under the action of a time dependent force given by $\vec{F} = (6t\hat{i} + 6t^{2}\hat{j})N$ . The power developed by the force at the time t is given by

A

$(6t^{4} + 9t^{5})W$

B

$(3t^{3} + 6t^{5})W$

C

$(9t^{5} + 6t^{3})W$

D

$(9t^{3} + 6t^{5})W$

Question 18: Palette 18/226

Errorless JEE (Main) April 2024 MCQ

If a rubber ball falls from a height h and rebounds up to the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are

A

$50\%, \sqrt{\frac{gh}{2}}$

B

$50\%, \sqrt{gh}$

C

$40\%, \sqrt{2gh}$

D

$50\%, \sqrt{2gh}$

Question 19: Palette 19/226

Errorless JEE (Main) April 2024 MCQ

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation $v = \alpha \sqrt{x}$ , where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be

A

$\frac{m}{2\alpha^{2}d}$

B

$\frac{md}{2\alpha^{2}}$

C

$\frac{m\alpha^{2}d}{2}$

D

$2m\alpha^{2}d$

Question 20: Palette 20/226

Errorless JEE (Main) April 2024 MCQ

A stationary particle breaks into two parts of masses $m_{A}$ and $m_{B}$ which move with velocities $v_{A}$ and $v_{B}$ respectively. The ratio of their kinetic energies ( $K_{B}:K_{A}$ ) is

A

$v_{B}:v_{A}$

B

$m_{B}:m_{A}$

C

$m_{B}v_{B}:m_{A}v_{A}$

D

1:1

Question 21: Palette 21/226

Errorless JEE (Main) April 2024 MCQ

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is

A

$1:\sqrt{3}:2$

B

$1:\sqrt{3}:\sqrt{2}$

C

$\sqrt{2}:\sqrt{3}:1$

D

$\sqrt{3}:\sqrt{2}:1$

Question 22: Palette 22/226

Errorless JEE (Main) April 2024 MCQ

The energy equivalent of 1 g of substance is

A

$11.2 \times 10^{24}$ MeV

B

$5.6 \times 10^{12}$ MeV

C

5.6 eV

D

$5.6 \times 10^{26}$ MeV

Question 23: Palette 23/226

Errorless JEE (Main) April 2024 MCQ

A body of $m$ kg slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is (given, R = 14 m, $g = 10m/s^{2}$ and $\sqrt{2} = 1.4$ )

A

19.8 m/s

B

21.9 m/s

C

16.7 m/s

D

10.6 m/s

Question 24: Palette 24/226

Errorless JEE (Main) April 2024 MCQ

Four particles A, B, C, D of mass $\frac{m}{2}$ , m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is

A

D

B

C

C

A

D

B

Question 25: Palette 25/226

Errorless JEE (Main) April 2024 MCQ

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be Case-1 : Pulled straight up Case-2 : Along the ramp

A

1:1

B

2:1

C

$\sqrt{3}:2$

D

1:2

Question 26: Palette 26/226

Errorless JEE (Main) April 2024 MCQ

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to

A

$t^{2}$

B

$t^{2/3}$

C

$t^{3/2}$

D

t

Question 27: Palette 27/226

Errorless JEE (Main) April 2024 MCQ

A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is

A

32%

B

44%

C

16%

D

84%

Question 28: Palette 28/226

Errorless JEE (Main) April 2024 MCQ

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be

A

$500\%$

B

$600\%$

C

$6\%$

D

$60\%$

Question 29: Palette 29/226

Errorless JEE (Main) April 2024 MCQ

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is

A

$\sqrt{6} m$

B

$2m$

C

$1m$

D

$\sqrt{5} m$

Question 30: Palette 30/226

Errorless JEE (Main) Jan. 2023 MCQ

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be $(g = 10m/s^{2})$

A

0

B

0.25 m/s

C

2 m/s

D

4 m/s

Question 31: Palette 31/226

Errorless JEE (Main) Jan. 2023 MCQ

Identify the correct statements from the following
(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
(C) Work done by friction on a body sliding down an inclined plane is positive.
(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.
(E) Work done by the air resistance on an oscillating pendulum is negative.
Choose the correct answer from the options given below

A

B and E only

B

A and C only

C

B, D and E only

D

B and D only

Question 32: Palette 32/226

Errorless JEE (Main) April 2023 MCQ

Two bodies are having kinetic energies in the ratio 16:9. If they have same linear momentum, the ratio of their masses respectively is

A

4:3

B

3:4

C

16:9

D

9:16

Question 33: Palette 33/226

Errorless JEE (Main) April 2023 MCQ

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity

A

v

B

$\frac{v}{2}$

C

$\frac{v}{3}$

D

$\frac{v}{4}$

Question 34: Palette 34/226

Errorless JEE (Main) April 2023 MCQ

Given below are two statements : Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of the above statements, choose the most appropriate answer from the options given below

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 35: Palette 35/226

Errorless JEE (Main) April 2023 MCQ

A bullet of mass 0.1 kg moving horizontally with speed $400 \, ms^{-1}$ hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is ____ (Given $g = 10 \, ms^{2}$ )

A

0.50

B

0.90

C

0.65

D

0.25

Question 36: Palette 36/226

Errorless JEE (Main) April 2023 MCQ

The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x}+1}$ , that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

A

2

B

4

C

2.4

D

16

Question 37: Palette 37/226

Errorless JEE (Advanced) 2023 MSQ

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity $\vec{u}_{0}=u_{0}\hat{x}$ and falls on the ground at a distance d from the building making an angle $\theta$ with the horizontal. It bounces off with a velocity $\vec{v}$ and reaches a maximum height $h_{1}$ . The acceleration due to gravity is g and the coefficient of restitution of the ground is $1/\sqrt{3}$ . Which of the following statement(s) is(are) correct

A

$\vec{u}_0 = \sqrt{2gh}\hat{x}$

B

$\vec{v} = \sqrt{2gh} (\hat{x} -\hat{z})$

C

$\theta = 60^{\circ}$

D

$d / h_{1} = 2\sqrt{3}$

Question 38: Palette 38/226

Errorless JEE (Main) June 2022 MCQ

A particle experiences a variable force $\vec{F} = (4x\hat{i} + 3y^2\hat{j})$ in a horizontal $x - y$ plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the $x - y$ plane, the kinetic energy changes by

A

$50.0J$

B

$12.5J$

C

$25.0J$

D

$0J$

Question 39: Palette 39/226

Errorless JEE (Main) June 2022 MCQ

In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when it reaches point 'B' is Ground

A

$\frac {1}{2} m g y _ {0} ^ {2}$

B

$\frac {1}{2} m g y ^ {2}$

C

$m g (y - y _ {0})$

D

$mgy_0$

Question 40: Palette 40/226

Errorless JEE (Main) June 2022 MCQ

Potential energy as a function of r is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$ , where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be

A

$\left(\frac{A}{B}\right)^{\frac{1}{5}}$

B

$\left(\frac{B}{A}\right)^{\frac{1}{5}}$

C

$\left(\frac{2A}{B}\right)^{\frac{1}{5}}$

D

$\left(\frac{B}{2A}\right)^{\frac{1}{5}}$

Question 41: Palette 41/226

Errorless JEE (Main) June 2022 MCQ

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass (Assume the collision to be head-on elastic collision)

A

$50.0\%$

B

$66.6\%$

C

$55.5\%$

D

$33.3\%$

Question 42: Palette 42/226

Errorless JEE (Main) June 2022 MCQ

A particle of mass 500 gm is moving in a straight line with velocity $v = bx^{5/2}$ . The work done by the net force during its displacement from x = 0 to x = 4m is (Take $b = 0.25 m^{-3/2} s^{-1}$ )

A

2 J

B

4 J

C

8 J

D

16 J

Question 43: Palette 43/226

Errorless JEE (Main) June 2022 MCQ

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

A

Zero

B

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

C

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

D

$mk^{2}rt$

Question 44: Palette 44/226

Errorless JEE (Main) July 2022 MCQ

A bullet of mass $200g$ having initial kinetic energy $90J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40J$ within 1s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is

A

45 m

B

90 m

C

125 m

D

25 m

Question 45: Palette 45/226

Errorless JEE (Main) July 2022 MCQ

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed $10 \, ms^{-1}$ gets embedded in it, then loss of kinetic energy will be

A

4.9 J

B

9.8 J

C

14.7 J

D

19.6 J

Question 46: Palette 46/226

Errorless JEE (Main) July 2022 MCQ

As per the given figure, two blocks each of mass 250g are connected to a spring of spring constant $2Nm^{-1}$ . If both are given velocity v in opposite directions, then maximum elongation of the spring is

A

$\frac{v}{2\sqrt{2}}$

B

$\frac{v}{2}$

C

$\frac{v}{4}$

D

$\frac{v}{\sqrt{2}}$

Question 47: Palette 47/226

Errorless JEE (Main) July 2022 MCQ

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

A

1:1

B

2:1

C

1:4

D

4:1

Question 48: Palette 48/226

Errorless JEE (Main) July 2022 MCQ

If momentum of a body is increased by 20%, then its kinetic energy increases by

A

36%

B

40%

C

44%

D

48%

Question 49: Palette 49/226

Errorless JEE (Main) July 2022 MCQ

Sand is being dropped from a stationary dropper at a rate of $0.5 \, kgs^{-1}$ on a conveyor belt moving with a velocity of $5 \, ms^{-1}$ . The power needed to keep belt moving with the same velocity will be

A

1.25 W

B

2.5 W

C

6.25 W

D

12.5 W

Question 50: Palette 50/226

Errorless JEE (Main) June 2022 MCQ

Arrange the four graphs in descending order of total work done; where $W_{1}, W_{2}, W_{3}$ and $W_{4}$ are the work done corresponding to figure 1, 2, 3 and 4 respectively Figure-1 $F\uparrow$ Figure-2 $F\uparrow$ Figure-3 $F\uparrow$ Figure-4 $F\uparrow$

A

$W_{3} > W_{2} > W_{1} > W_{4}$

B

$W_{3} > W_{2} > W_{4} > W_{1}$

C

$W_{2} > W_{3} > W_{4} > W_{1}$

D

$W_{2} > W_{3} > W_{1} > W_{4}$

Question 51: Palette 51/226

Errorless JEE (Main) July 2022 MCQ

A bullet is shot vertically downwards with an initial velocity of 100 m/s from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t = 20 s will be (Take $g = 10 \, m/s^{2}$ )

A

a

B

b

C

c

D

d

Question 52: Palette 52/226

Errorless JEE (Main) Feb. 2021 MCQ

Given below are two statements: one is labelled as assertion A and the other is labelled as reason R Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 53: Palette 53/226

Errorless JEE (Main) March 2021 MCQ

An object of mass $m_{1}$ collides with another object of mass $m_{2}$ , which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m_{2}:m_{1}$ is

A

3:1

B

2:1

C

1:2

D

1:1

Question 54: Palette 54/226

Errorless JEE (Main) March 2021 MCQ

A large block of wood of mass $M = 5.99 \, kg$ is hanging from two long massless cords. A bullet of mass $m = 10g$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $h = 9.8 \, cm$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is (Take $g = 9.8 \, ms^{-2}$ )

A

841.4 m/s

B

811.4 m/s

C

831.4 m/s

D

821.4 m/s

Question 55: Palette 55/226

Errorless JEE (Main) March 2021 MCQ

A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of $20 \, ms^{-1}$ . The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now

A

$19.0 \, ms^{-1}$

B

$4.47 \, ms^{-1}$

C

$14.41 \, ms^{-1}$

D

$1.00 \, ms^{-1}$

Question 56: Palette 56/226

Errorless JEE (Main) March 2021 MCQ

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to

A

$t^{2/3}$

B

$t^{3/2}$

C

t

D

$t^{1/2}$

Question 57: Palette 57/226

Errorless JEE (Main) July 2021 MCQ

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the workdone by the porter in lowering the suitcase (take $g = 9.8 ms^{-2}$ )

A

-62720.0 J

B

-627.2 J

C

+627.2 J

D

784.0 J

Question 58: Palette 58/226

Errorless JEE (Main) July 2021 MCQ

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 m and 2 m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is

A

6 m/s

B

9 m/s

C

4 m/s

D

3 m/s

Question 59: Palette 59/226

Errorless JEE (Main) July 2021 MCQ

Given below is the plot of a potential energy function $U(x)$ for a system, in which a particle is in one dimensional motion, while a conservative force $F(x)$ acts on it. Suppose that $E_{mech} = 8J$ , the incorrect statement for this system is [where K.E. = kinetic energy]

A

At $x > x_{4}$ K.E. is constant throughout the region

B

At $x < x_{1}$ , K.E. is smallest and the particle is moving at the slowest speed

C

At $x = x_{2}$ , K.E. is
greatest and the particle is moving at the fastest speed

D

At $x = x_{3}$ , K.E. $= 4J$

Question 60: Palette 60/226

Errorless JEE (Main) July 2021 MCQ

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by

A

$\left(\frac{9P}{8m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$

B

$\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{2}{3}}$

C

$\left(\frac{9m}{8P}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$

D

$\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$

Question 61: Palette 61/226

Errorless JEE (Main) Aug. 2021 MCQ

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of $0.8\sqrt{gh}$ . The value of work done by the air – friction is

A

-0.68 mgh

B

0.64 mgh

C

mgh

D

1.64 mgh

Question 62: Palette 62/226

Errorless JEE (Main) Aug. 2021 MCQ

A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1:2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is

A

$\frac{1}{8}$

B

$\frac{2}{3}$

C

$\frac{1}{3}$

D

$\frac{1}{4}$

Question 63: Palette 63/226

Errorless JEE (Main) Jan. 2020 MCQ

A 60 HP electric motor lifts an elevator having a maximum total load capacity of $2000\mathrm{kg}$ . If the frictional force on the elevator is $4000N$ , the speed of the elevator at full load is close to $(1\mathrm{HP} = 746W, g = 10ms^{-2})$

A

$1.7ms^{-1}$

B

$2.0ms^{-1}$

C

$1.9ms^{-1}$

D

$1.5ms^{-1}$

Question 64: Palette 64/226

Errorless JEE (Main) Jan. 2020 MCQ

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

A

$56300W$

B

$48000W$

C

$66000W$

D

$62360W$

Question 65: Palette 65/226

Errorless JEE (Main) Jan. 2020 MCQ

A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$ . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is

A

$\frac{1}{2}$

B

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

C

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

D

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

Question 66: Palette 66/226

Errorless JEE (Main) Jan. 2020 MCQ

Two particles of equal mass m have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right)$ . They collide completely inelastically. The energy lost in the process is

A

$3/4mu^{2}$

B

$1/8mu^{2}$

C

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

D

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

Question 67: Palette 67/226

Errorless JEE (Main) Jan. 2020 MCQ

A particle of mass m is projected with a speed u from the ground at an angle $\theta=\frac{\pi}{3}w.r.t.$ horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\hat{i}$ . The horizontal distance covered by the combined mass before reaching the ground is

A

$\frac{3\sqrt{2}}{4}\frac{u^{2}}{g}$

B

$2\sqrt{2}\frac{u^{2}}{g}$

C

$\frac{3\sqrt{3}}{8}\frac{u^{2}}{g}$

D

$\frac{5}{8}\frac{u^{2}}{g}$

Question 68: Palette 68/226

Errorless JEE (Main) Sep. 2020 MCQ

A particle of mass m with an initial velocity $u\hat{i}$ collides perfectly elastically with a mass 3m at rest. It moves with a velocity $v\hat{j}$ after collision, then v is given by

A

$v = \sqrt{\frac{2}{3}}u$

B

$v = \frac{u}{\sqrt{3}}$

C

$v = \frac{1}{\sqrt{6}}u$

D

$v = \frac{u}{\sqrt{2}}$

Question 69: Palette 69/226

Errorless JEE (Main) Sep. 2020 MCQ

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take $g = 10m/s^{2}$ . Assume there is no rotational motion and loss of energy after the collision is negligible]

A

21 J

B

23 J

C

20 J

D

19 J

Question 70: Palette 70/226

Errorless JEE (Main) Sep. 2020 MCQ

Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of ‘p’ is close to

A

77

B

37

C

87

D

94

Question 71: Palette 71/226

Errorless JEE (Main) Sep. 2020 MCQ

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15m. 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

5250 J

B

3280 J

C

2780 J

D

5690 J

Question 72: Palette 72/226

Errorless JEE (Main) Sep. 2020 MCQ

Particle A of mass $m_{1}$ moving with velocity $(\sqrt{3}\hat{i}+\hat{j})ms^{-1}$ collides with another particle B of mass $m_{2}$ which is at rest initially. Let $\vec{v}_{1}$ and $\vec{v}_{2}$ be the velocities of particles A and B after collision respectively. If $m_{1}=2m_{2}$ and after collision $\vec{v}_{1}=(\hat{i}+\sqrt{3}\hat{j})ms^{-1}$ , the angle between $\vec{v}_{1}$ and $\vec{v}_{2}$ is

A

60°

B

15°

C

-45°

D

105°

Question 73: Palette 73/226

Errorless JEE (Main) Sep. 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 74: Palette 74/226

Errorless JEE (Main) Sep. 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 is (all quantities are in SI units)

A

3/2

B

1

C

2

D

1/2

Question 75: Palette 75/226

Errorless JEE (Main) Jan. 2019 MCQ

A force acts on a 2kg 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

850 J

B

900 J

C

950 J

D

875 J

Question 76: Palette 76/226

Errorless JEE (Main) Jan. 2019 MCQ

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an brutal speed v towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically $\frac{5}{6}th$ of the initial kinetic energy is lost in whole process. What is value of M/m

A

4

B

5

C

3

D

2

Question 77: Palette 77/226

Errorless JEE (Main) Jan. 2019 MCQ

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg if fired vertically upward, with a velocity $100 \, ms^{-1}$ , from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is $(g = 10 \, ms^{-2})$

A

30 m

B

10 m

C

40 m

D

20 m

Question 78: Palette 78/226

Errorless JEE (Main) Jan. 2019 MCQ

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

A

Zero

B

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

C

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

D

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

Question 79: Palette 79/226

Errorless JEE (Main) Jan. 2019 MCQ

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

A

$15J$

B

$10J$

C

$12J$

D

$9J$

Question 80: Palette 80/226

Errorless JEE (Main) Jan. 2019, June 2022 MCQ

A body of mass 1 kg falls freely from a height of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant $k = 1.25 \times 10^{6} N/m$ . The body sticks to the platform and the spring's maximum compression is found to be x. Given that $g = 10 ms^{-2}$ , the value of x will be close to

A

2 cm

B

8 cm

C

80 cm

D

40 cm

Question 81: Palette 81/226

Errorless JEE (Main) Jan. 2019 MCQ

An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus

A

4 m

B

3.5 m

C

2 m

D

1.5 m

Question 82: Palette 82/226

Errorless JEE (Main) April 2019 MCQ

A body of mass $m_{1}$ moving with an unknown velocity of $v_{1}\hat{i}$ , undergoes a collinear collision with a body of mass $m_{2}$ moving with a velocity $v_{2}\hat{i}$ . After collision, $m_{1}$ and $m_{2}$ move with velocities of $v_{3}\hat{i}$ and $v_{4}\hat{i}$ , respectively. If $m_{2}=0.5m_{1}$ and $v_{3}=0.5v_{1}$ , then $v_{1}$ is

A

$v_{4}-\frac{v_{2}}{4}$

B

$v_{4}-\frac{v_{2}}{2}$

C

$v_{4}-v_{2}$

D

$v_{4}+v_{2}$

Question 83: Palette 83/226

Errorless JEE (Main) April 2019 MCQ

A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such that its $\left(\frac{1}{n}\right)^{th}$ 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

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

C

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

D

nMgL

Question 84: Palette 84/226

Errorless JEE (Main) April 2019 MCQ

A particle of mass ‘m’ is moving with speed ‘2v’ and collides with a mass ‘2m’ moving with speed ‘v’ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass ‘m’, which move at angle $45^{\circ}$ with respect to the original direction. The speed of each of the moving particle will be

A

$v/(2\sqrt{2})$

B

$2\sqrt{2}v$

C

$\sqrt{2}v$

D

$v/\sqrt{2}$

Question 85: Palette 85/226

Errorless JEE (Main) April 2019 MCQ

A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by

A

$\frac{2v^{2}}{7g}$

B

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

C

$\frac{2v^{2}}{5g}$

D

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

Question 86: Palette 86/226

Errorless JEE (Main) April 2019 MCQ

Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds $\nu_{1}$ and $\nu_{2}$ , respectively. The values of $\nu_{1}$ and $\nu_{2}$ are nearly

A

3.2 m/s and 6.3 m/s

B

3.2 m/s and 12.6 m/s

C

6.5 m/s and 6.3 m/s

D

6.5 m/s and 3.2 m/s

Question 87: Palette 87/226

Errorless JEE (Main) April 2019 MCQ

A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body

A

1.8 kg

B

1.2 kg

C

1.5 kg

D

1.0 kg

Question 88: Palette 88/226

Errorless JEE (Main) April 2019 MCQ

A particle moves in the 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 3m is

A

6.5 J

B

2.5 J

C

4 J

D

5 J

Question 89: Palette 89/226

Errorless JEE (Advanced) 2019 MSQ

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $L = L_{0}$ the particle speed is $v = v_{0}$ . The piston is moved inward at a very low speed V such that $V \ll \frac{dL}{L} v_{0}$ , where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct

A

The rate of which the particle strikes the piston is v/L

B

After each collision with the piston, the particle speed increases by 2V

C

The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from $L_0$ to $\frac{1}{2} L_0$

D

If the piston moves inward by dL, the particle speed increases by $2v\frac{dL}{L}$

Question 90: Palette 90/226

Errorless NEET 2018 MCQ

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to

A

$\frac{3}{2} D$

B

$D$

C

$\frac{7}{5} D$

D

$\frac{5}{4} D$

Question 91: Palette 91/226

Errorless JEE (Main) 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

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

B

Zero

C

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

D

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

Question 92: Palette 92/226

Errorless JEE (Main) 2018 MCQ

In a collinear collision, a particle with an initial speed $v_{0}$ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is

A

$\sqrt{2}v_{0}$

B

$\frac{v_{0}}{2}$

C

$\frac{v_{0}}{\sqrt{2}}$

D

$\frac{v_{0}}{4}$

Question 93: Palette 93/226

Errorless JEE (Main) 2018 MCQ

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_d$ ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_c$ . The values of $p_d$ and $p_c$ are respectively

A

(.28, .89)

B

(0, 0)

C

(0, 1)

D

(.89, .28)

Question 94: Palette 94/226

Errorless JEE (Advanced) 2018 MSQ

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$ -axis. Its kinetic energy $K$ changes with time as $dK / dt = \gamma t$ , where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true

A

The force applied on the particle is constant

B

The speed of the particle is proportional to time

C

The distance of the particle from the origin increases linearly with time

D

The force is conservative

Question 95: Palette 95/226

Errorless JEE (Main) 2017 MCQ

A particle $A$ of mass $m$ and initial velocity $\nu$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $\lambda_{A}$ to $\lambda_{B}$ after the collision is

A

$\frac{\lambda_A}{\lambda_B} = \frac{1}{2}$

B

$\frac{\lambda_A}{\lambda_B} = \frac{1}{3}$

C

$\frac{\lambda_A}{\lambda_B} = 2$

D

$\frac{\lambda_A}{\lambda_B} = \frac{2}{3}$

Question 96: Palette 96/226

Errorless JEE (Advanced) 2017 MSQ

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x=0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and its slides down. When the mass loses contact with the block, its position is x and the velocity is v. At the instant, which of the following options is/are correct

A

The velocity of the point mass $m$ is: $v = \sqrt{\frac{2gR}{1 + \frac{m}{M}}}$

B

The $x$ component of displacement of the center of mass of the block $M$ is: $-\frac{mR}{M + m}$

C

The position of the point mass is: $x = -\sqrt{2}\frac{mR}{M + m}$

D

The velocity of the block $M$ is: $V = -\frac{m}{M}\sqrt{2gR}$

Question 97: Palette 97/226

Errorless JEE (Main) 2016 MCQ

A point particle of mass m, 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 $\mathbf{P}_{\bullet}$ .

A

0.2 and $3.5m$

B

0.29 and $3.5m$

C

0.29 and $6.5m$

D

0.2 and $6.5m$

Question 98: Palette 98/226

Errorless NEET (Phase-II) 2016 MCQ

A bullet of mass 10 g moving horizontally with a velocity of $400 \, ms^{-1}$ strikes of wooden block of mass 2kg which is suspended by a light inextensible string of length 5m. As a result the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be

A

$160 \, ms^{-1}$

B

$100 \, ms^{-1}$

C

$80 \, ms^{-1}$

D

$120 \, ms^{-1}$

Question 99: Palette 99/226

Errorless JEE (Main) 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

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

B

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

C

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

D

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

Question 100: Palette 100/226

Errorless NEET (Phase-II) 2016 MCQ

Two identical balls A and B having velocities of 0.5 m/s and -0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be

A

0.3 m/s and 0.5 m/s

B

-0.5 m/s and 0.3 m/s

C

0.5 m/s and -0.3 m/s

D

-0.3 m/s and 0.5 m/s

Question 101: Palette 101/226

Errorless JEE (Main) 2015 MCQ

A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

A

44%

B

50%

C

56%

D

62%

Question 102: Palette 102/226

Errorless JEE (Main) 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 103: Palette 103/226

Errorless CBSE PMT 2014 MCQ

A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is

A

$2mv^{2}$

B

$4mv^{2}$

C

$mv^{2}$

D

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

Question 104: Palette 104/226

Errorless JEE (Advanced) 2014 MCQ

A wire, which passes through the hole is 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 105: Palette 105/226

Errorless JEE (Advanced) 2014 MCQ

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale

A

B

C

D

Question 106: Palette 106/226

Errorless JEE (Advanced) 2013 MCQ

The work done on a particle of mass m by a force, $K\left[\frac{x}{(x^{2}+y^{2})^{3/2}}\hat{i}+\frac{y}{(x^{2}+y^{2})^{3/2}}\hat{j}\right]$ (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 107: Palette 107/226

Errorless WB-JEE 2013 MCQ

A particle is acted upon by a constant power. Then, which of the following physical quantity remains constant

A

Speed

B

Rate of change of acceleration

C

Kinetic energy

D

Rate of change of kinetic energy

Question 108: Palette 108/226

Errorless JEE (Advanced) 2013 MSQ

A particle of mass $m$ is attached to one end of a mass-less spring of force constant $k$ , lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t = 0$ with an initial velocity $u_0$ . When the speed of the particle is $0.5u_0$ , it collides elastically with a rigid wall. After this collision

A

The speed of the particle when it returns to its equilibrium position is $u_{0}$

B

The time at which the particle passes through the equilibrium position for the first time is $t = \pi \sqrt{\frac{m}{k}}$

C

The time at which the maximum compression of the spring occurs is $t = \frac{4\pi}{3}\sqrt{\frac{m}{k}}$

D

The time at which the particle passes throughout the equilibrium position for the second time is $t = \frac{5\pi}{3}\sqrt{\frac{m}{k}}$

Question 109: Palette 109/226

Errorless JEE (Main) 2013 MCQ

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

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 110: Palette 110/226

Errorless JEE (Advanced) 2013 MCQ

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 below, 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

$5ms^{-1}$

B

$10ms^{-1}$

C

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

D

$20ms^{-1}$

Question 111: Palette 111/226

Errorless JEE (Advanced) 2013 MCQ

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 below, 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

$7.5N$

B

$8.6N$

C

$11.5N$

D

$22.5N$

Question 112: Palette 112/226

Errorless CBSE PMT (Pre.) 2012 MCQ

Two spheres $A$ and $B$ of masses $m_1$ and $m_2$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $v$ along $x$ -axis. After collision $B$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction

A

Same as that of $B$

B

Opposite to that of $B$

C

$\theta = \tan^{-1}(1/2)$ to the $x$ -axis

D

$\theta = \tan^{-1}(-1/2)$ to the $x$ -axis

Question 113: Palette 113/226

Errorless Kerala PET 2012 MCQ

A girl in a swing is 2.5m above ground at the maximum height and at 1.5m above the ground at the lowest point. Her maximum velocity in the swing is $(g=10ms^{-2})$

A

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

B

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

C

$2\sqrt{3}ms^{-1}$

D

$3\sqrt{2}ms^{-1}$

E

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

Question 114: Palette 114/226

Errorless CBSE PMT (Mains) 2012 MCQ

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

A

68%

B

41%

C

200%

D

100%

Question 115: Palette 115/226

Errorless MP PET 2012 MCQ

A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments each of mass m are found to move with a speed 'v' each in mutually perpendicular directions. The total energy released in this process

A

0

B

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

C

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

D

$2mv^{2}$

Question 116: Palette 116/226

Errorless CBSE PMT (Mains) 2012 MCQ

A car of mass m starts from rest and accelerates so that instantaneous power delivered to the car has a constant magnitude $P_{0}$ . The instantaneous velocity of this car is proportional to

A

$t^{2}P_{0}$

B

$t^{1/2}$

C

$t^{-1/2}$

D

$\frac{t}{\sqrt{m}}$

Question 117: Palette 117/226

Errorless Kerala PET 2012 MCQ

The shape of the curve representing the relation between the speed and kinetic energy of a moving object is

A

Parabola

B

Ellipse

C

Straight line with positive slope

D

Straight line with negative slope

E

Exponential

Question 118: Palette 118/226

Errorless Odisha JEE 2011, 12 MCQ

A block of mass 5kg is resting on a smooth surface. At what angle a force of 20N be acted on the body so that it will acquired a kinetic energy of 40J after moving 4m

A

30°

B

45°

C

60°

D

120°

Question 119: Palette 119/226

Errorless CBSE PMT (Pre.) 2011 MCQ

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

A

At the instant just after the body is projected

B

At the highest position of the body

C

At the instant just before the body hits the earth

D

It remains constant all through

Question 120: Palette 120/226

Errorless Kerala PET 2011 MCQ

A ball dropped from a height of 2m rebounds to a height of 1.5m after hitting the ground. Then the percentage of energy lost is

A

25

B

30

C

50

D

100

E

200

Question 121: Palette 121/226

Errorless Odisha JEE 2011 MCQ

Two masses of 0.25kg each moves towards each other with speed $3ms^{-1}$ and $1ms^{-1}$ collide and stick together. Find the final velocity

A

$0.5ms^{-1}$

B

$2ms^{-1}$

C

$1ms^{-1}$

D

$0.25ms^{-1}$

Question 122: Palette 122/226

Errorless AIEEE 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 constants and x is the distance between the atoms. If the dissociation energy of the molecule is $D=[U(x=\infty)-U_{\mathrm{at equilibrium}}]$ , D is

A

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

B

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

C

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

D

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

Question 123: Palette 123/226

Errorless J & K CET 2010 MCQ

The energy associated with one gram of mass is

A

$9 \times 10^{-13} J$

B

$9 \times 10^{-16} J$

C

$9 \times 10^{13} J$

D

$9 \times 10^{16} J$

Question 124: Palette 124/226

Errorless MP PET 2010 MCQ

A body of mass $M$ is moving with a uniform speed of $10m / s$ on frictionless surface under the influence of two forces $F_{1}$ and $F_{2}$ . The net power of the system is

A

$10F_{1}F_{2}M$

B

$10(F_{1} + F_{2})M$

C

$(F_{1} + F_{2})M$

D

Zero

Question 125: Palette 125/226

Errorless CBSE PMT 2010 MCQ

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine

A

800 W

B

400 W

C

200 W

D

100 W

Question 126: Palette 126/226

Errorless CBSE PMT 2010 MCQ

A ball moving with velocity 2 m/s. collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s.) after collision will be

A

0, 2

B

0, 1

C

1, 1

D

1, 0.5

Question 127: Palette 127/226

Errorless Odisha JEE 2010 MCQ

In an inelastic collision

A

Only momentum is conserved

B

Only kinetic energy is conserved

C

Neither momentum nor kinetic energy is conserved

D

Both momentum and kinetic energy are conserved

Question 128: Palette 128/226

Errorless J & K CET 2010 MCQ

Three identical spherical balls $A, B$ and $C$ are placed on a table as shown in the figure along a straight line. $B$ and $C$ are at rest initially. The ball A hits B head on with a speed of $10 \, m \, s^{-1}$ . Then after all collisions (assumed to be elastic) A and B are brought to rest and C takes off with a velocity of

A

$5 \, m \, s^{-1}$

B

$10 \, m \, s^{-1}$

C

$2.5 \, m \, s^{-1}$

D

$7.5 \, m \, s^{-1}$

Question 129: Palette 129/226

Errorless Kerala PMT 2010 MCQ

The potential energy of a conservative system is given by $V(x) = (x^{2} - 3x)$ joule. Then its equilibrium position is at

A

x = 1.5 m

B

x = 2 m

C

x = 2.5 m

D

x = 3 m

E

x = 0.33 m

Question 130: Palette 130/226

Errorless IIT-JEE 2010 MCQ

A block of mass 2 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 seconds is

A

4.50 J

B

7.50 J

C

5.06 J

D

14.06 J

Question 131: Palette 131/226

Errorless IIT-JEE 2010 MSQ

A point mass of 1 kg collides with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of $2ms^{-1}$ . Which of the following statement(s) is (are) correct for the system of these two masses

A

Total momentum of the system is 3 kg ms $^{-1}$

B

Momentum of 5 kg mass after collision is 4 kg ms $^{-1}$

C

Kinetic energy of the centre of mass is 0.75 J

D

Total kinetic energy of the system is 4 J

Question 132: Palette 132/226

Errorless AIEEE 2010 MCQ

Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 133: Palette 133/226

Errorless CBSE PMT 2009 MCQ

A body of mass 1 kg is thrown upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction ( $g = 10 \, m/s^{2}$ )

A

20 J

B

30 J

C

40 J

D

10 J

Question 134: Palette 134/226

Errorless EAMCET 2009 MCQ

A bullet of mass 0.02 kg travelling horizontally with velocity $250 \, ms^{-1}$ strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of 40m. The coefficient of sliding friction of the rough surface is ( $g = 9.8 \, ms^{-2}$ )

A

0.75

B

0.61

C

0.51

D

0.30

Question 135: Palette 135/226

Errorless EAMCET 2009 MCQ

A motor of power $p_{0}$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe n times, the power of the motor is increased to $p_{1}$ . The ratio of $p_{1}$ to $p_{0}$ is

A

n:1

B

$n^{2}:1$

C

$n^{3}:1$

D

$n^{4}:1$

Question 136: Palette 136/226

Errorless IIT-JEE 2009 MCQ

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C

A

3 m/s

B

4 m/s

C

5 m/s

D

1 m/s

Question 137: Palette 137/226

Errorless Kerala PET 2009 MCQ

A particle is acted upon by a force F which varies with position x as shown in figure. If the particle at x = 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x = 16 m is

A

$45\mathrm{J}$

B

$30\mathrm{J}$

C

70 J

D

135 J

E

20 J

Question 138: Palette 138/226

Errorless KCET 2009 MCQ

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is

A

225 J

B

200 J

C

400 J

D

175 J

Question 139: Palette 139/226

Errorless WB-JEE 2009 MCQ

The force $F$ acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the $1^{\text{st}}$ meter of the trajectory

A

5 J

B

10 J

C

15 J

D

2.5 J

Question 140: Palette 140/226

Errorless AIEEE 2009 MCQ

Consider a rubber ball freely falling from a height h=4.9m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be

A

B

C

D

Question 141: Palette 141/226

Errorless WB-JEE 2008 MCQ

A wire is stretched under a force. If the wire suddenly snaps the temperature of the wire

A

Remains the same

B

Decreases

C

Increases

D

First decreases then increases

Question 142: Palette 142/226

Errorless Kerala PET 2008 MCQ

A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, the velocity of the ball is

A

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

B

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

C

$40 \mathrm{~ms}^{-1}$

D

$60 \mathrm{~ms}^{-1}$

E

$90 \mathrm{~ms}^{-1}$

Question 143: Palette 143/226

Errorless Kerala PET 2008 MCQ

A bullet of mass 0.05 kg moving with a speed of $80 \, ms^{-1}$ enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the bullet is

A

300 N

B

20 N

C

400 N

D

40 N

E

200 N

Question 144: Palette 144/226

Errorless AIEEE 2008 MCQ

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

A

$2 \times 10^{5} J - 3 \times 10^{5} J$

B

20,000 J - 50,000 J

C

2,000 J - 5,000 J

D

200 J - 500 J

Question 145: Palette 145/226

Errorless CBSE PMT 2008 MCQ

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine ( $g=10\ m/s^{2}$ )

A

12.3 kW

B

7.0 kW

C

8.1 kW

D

10.2 kW

Question 146: Palette 146/226

Errorless Odisha JEE 2008 MCQ

Two identical mass $M$ moving with velocity $u_{1}$ and $u_{2}$ collide perfectly inelastically. The loss in energy is

A

$\frac{M}{2}(u_2 - u_1)^2$

B

$\frac{M}{2}(u_1 - u_2)^2$

C

$\frac{M}{4}(u_1 - u_2)^2$

D

$\frac{M}{4}(u_2 - u_1)^2$

Question 147: Palette 147/226

Errorless IIT-JEE 2008 MSQ

Two balls, having linear momenta $\vec{p}_1 = p\hat{i}$ and $\vec{p}_2 = -\vec{p}\hat{i}$ , undergo a collision in free space. There is no external force acting on the balls. Let $\vec{p}_1$ and $\vec{p}_2$ be their final momenta. The following option(s) is(are) NOT ALLOWED for any non-zero value of $p, a_1, a_2, b_1, b_2, c_1$ and $c_2$

A

$\vec{p}_1 = a_1\hat{i} +b_1\hat{j} +c_1\hat{k},\vec{p}_2 = a_2\hat{i} +b_2\hat{j}$

B

$\vec{p}_1 = c_1\hat{k}$ , $\vec{p}_2 = c_2\hat{k}$

C

$\vec{p}_1 = a_1\hat{i} +b_1\hat{j} +c_1\hat{k},\vec{p}_2 = a_2\hat{i} +b_2\hat{j} -c_1\hat{k}$

D

$\vec{p}_1 = a_1\hat{i} +b_1\hat{j},\vec{p}_2 = a_2\hat{i} +b_1\hat{j}$

Question 148: Palette 148/226

Errorless IIT-JEE 2008 MCQ

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60^{\circ}$ to $30^{\circ}$ at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic ( $g = 10 \, m/s^{2}$ ). The speed of the block at point B immediately after it strikes the second incline is

A

$\sqrt{60}$ m/s

B

$\sqrt{45}$ m/s

C

$\sqrt{30}$ m/s

D

$\sqrt{15}$ m/s

Question 149: Palette 149/226

Errorless IIT-JEE 2008 MCQ

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60^{\circ}$ to $30^{\circ}$ at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic ( $g = 10 \, m/s^{2}$ ). The speed of the block at point C, immediately before it leaves the second incline is

A

$\sqrt{120} m / s$

B

$\sqrt{105} m / s$

C

$\sqrt{90} m / s$

D

$\sqrt{75} m / s$

Question 150: Palette 150/226

Errorless IIT-JEE 2008 MCQ

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60^{\circ}$ to $30^{\circ}$ at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic ( $g = 10 \, m/s^{2}$ ). If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is

A

$\sqrt{30}$ m/s

B

$\sqrt{15}$ m/s

C

0

D

$-\sqrt{15}$ m/s

Question 151: Palette 151/226

Errorless Kerala PET 2007 MCQ

A rod AB of mass 10kg and length 4m rests on a horizontal floor with end A fixed so as to rotate it in vertical plane about perpendicular axis passing through A. If the work done on the rod is 100J, the height to which the end B be raised vertically above the floor is

A

1.5 m

B

2.0 m

C

1.0 m

D

2.5 m

Question 152: Palette 152/226

Errorless Kerala PET 2007 MCQ

A simple pendulum is released from $A$ as shown. If $m$ and $l$ represent the mass of the bob and length of the pendulum, the gain in kinetic energy at $B$ is

A

$\frac{mgl}{2}$

B

$\frac{mgl}{\sqrt{2}}$

C

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

D

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

Question 153: Palette 153/226

Errorless Kerala PET 2007 MCQ

A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

A

$\frac{S}{4}, \frac{3gS}{2}$

B

$\frac{S}{4}, \frac{\sqrt{3gS}}{2}$

C

$\frac{S}{2}, \frac{\sqrt{3gS}}{2}$

D

$\frac{S}{4} \cdot \sqrt{\frac{3gS}{2}}$

Question 154: Palette 154/226

Errorless AIEEE 2007 MCQ

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by

A

5.5 cm

B

2.5 cm

C

11.0 cm

D

8.5 cm

Question 155: Palette 155/226

Errorless Kerala PET 2007 MCQ

An electric pump is used to fill an overhead tank of capacity $9m^{3}$ kept at a height of $10m$ above the ground. If the pump takes 5 minutes to fill the tank by consuming $10kW$ power the efficiency of the pump should be (Take $g = 10ms^{-2}$ )

A

$60\%$

B

$40\%$

C

$20\%$

D

$30\%$

Question 156: Palette 156/226

Errorless KCET 2007 MCQ

A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3. The smaller fragment moves with a velocity of $6 \, ms^{-1}$ . The kinetic energy of the larger fragment is

A

96 J

B

216 J

C

144 J

D

360 J

Question 157: Palette 157/226

Errorless IIT-JEE 2007 MCQ

Statement-1 : In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Statement-2 : In an elastic collision, the linear momentum of the system is conserved.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 158: Palette 158/226

Errorless 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 assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 159: Palette 159/226

Errorless AIEEE 2006 MCQ

A particle of mass 100g is thrown vertically upwards with a speed of 5m/s. The work done by the force of gravity during the time the particle goes up is

A

-1.25 J

B

1.25 J

C

0.5 J

D

-0.5 J

Question 160: Palette 160/226

Errorless J & K CET 2006 MCQ

A body at rest breaks into two pieces with unequal mass

A

Both of them have equal speeds

B

Both of them move along a same line with unequal speeds

C

Sum of their momentum is non zero

D

They move along different lines with different speeds

Question 161: Palette 161/226

Errorless J & K CET 2006 MCQ

A body of mass 2 kg is projected at 20 m/s at an angle $60^{\circ}$ above the horizontal. Power on the block due to the gravitational force at its highest point is

A

200 W

B

$100\sqrt{3}$ W

C

50 W

D

Zero

Question 162: Palette 162/226

Errorless BHU 2006 MCQ

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to

A

$t^{1/2}$

B

$t$

C

$t^{3/2}$

D

$t^2$

Question 163: Palette 163/226

Errorless DCE 2006 MCQ

An intense stream of water of cross-sectional area A strikes a wall at an angle $\theta$ with the normal to the wall and returns back elastically. If the density of water is $\rho$ and its velocity is v, then the force exerted in the wall will be

A

$2 A v \rho \cos \theta$

B

$2 A v ^ {2} \rho \cos \theta$

C

$2 A v ^ {2} \rho$

D

$2 A v \rho$

Question 164: Palette 164/226

Errorless AIEEE 2006 MCQ

A mass of $Mkg$ is suspended by a weightless string, the horizontal force that is required to displace it until the string makes an angle of $45^{\circ}$ with the initial vertical direction is

A

$Mg\sqrt{2}$

B

$\frac{Mg}{\sqrt{2}}$

C

$Mg(\sqrt{2} - 1)$

D

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

Question 165: Palette 165/226

Errorless IIT-JEE 2006 MSQ

A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. Surface BC is frictionless. $K_{A}$ , $K_{B}$ and $K_{C}$ are kinetic energies of the ball at A, B and C, respectively, Then

A

$h_A > h_C:K_B > K_C$

B

$h _ {A} > h _ {C}: K _ {C} > K _ {A}$

C

$h_{A}=h_{C}:K_{B}=K_{C}$

D

$h_{A}<h_{C}:K_{A}>K_{C}$

Question 166: Palette 166/226

Errorless Kerala PET 2005 MCQ

A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is

A

$1:2:3$

B

$1:4:9$

C

$1:3:5$

D

$1:5:3$

Question 167: Palette 167/226

Errorless AIEEE 2005 MCQ

The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is

A

Zero

B

$\frac{ML^2}{K}$

C

$\sqrt{MK} L$

D

$\frac{KL^2}{2M}$

Question 168: Palette 168/226

Errorless AIEEE 2005; AIIMS 2007 MCQ

A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It slides down a smooth surface to the ground, then climbs up another hill of height 30 m and finally slides down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is

A

10 m/s

B

$10\sqrt{30}$ m/s

C

40 m/s

D

20 m/s

Question 169: Palette 169/226

Errorless J & K CET 2005; NEET (Karnataka) 2013 MCQ

A man does a given amount of work in 10 sec. Another man does the same amount of work in 20 sec. The ratio of the output power of first man to the second man is

A

1

B

1/2

C

2/1

D

None of these

Question 170: Palette 170/226

Errorless J & K CET 2005 MCQ

If the heart pushes 1 cc of blood in one second under pressure $20000 \, N/m^{2}$ the power of heart is

A

0.02 W

B

400 W

C

$5 \times 10^{-10} \, W$

D

0.2 W

Question 171: Palette 171/226

Errorless BCECE 2004 MCQ

A ball of mass m moves with speed v and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is

A

Zero

B

mv J

C

m/v.J

D

v/m J

Question 172: Palette 172/226

Errorless DCE 2004 MCQ

A man starts walking from a point on the surface of earth (assumed smooth) and reaches diagonally opposite point. What is the work done by him

A

Zero

B

Positive

C

Negative

D

Nothing can be said

Question 173: Palette 173/226

Errorless AIEEE 2004 MCQ

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

A

Its velocity is constant

B

Its acceleration is constant

C

Its kinetic energy is constant

D

It moves in a straight line

Question 174: Palette 174/226

Errorless AIEEE 2004 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

$x^2$

B

$e^x$

C

$x$

D

$\log_e x$

Question 175: Palette 175/226

Errorless UPSEAT 2004 MCQ

An object of mass 3m splits into three equal fragments. Two fragments have velocities $v\hat{j}$ and $v\hat{i}$ . The velocity of the third fragment is

A

$v(\hat{j}-\hat{i})$

B

$v(\hat{i}-\hat{j})$

C

$-v(\hat{i}+\hat{j})$

D

$\frac{v(\hat{i}+\hat{j})}{\sqrt{2}}$

Question 176: Palette 176/226

Errorless AFMC 2004; Odisha JEE 2008 MCQ

A rifle bullet loses $1/20^{\text{th}}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

A

5

B

10

C

11

D

20

Question 177: Palette 177/226

Errorless DCE 2004 MCQ

A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses 1 g and 3 g. The total K.E. of the fragments is $6.4 \times 10^{4}$ J. What is the K.E. of the smaller fragment

A

$2.5 \times 10^{4}$ J

B

$3.5 \times 10^{4}$ J

C

$4.8 \times 10^{4}$ J

D

$5.2 \times 10^{4}$ J

Question 178: Palette 178/226

Errorless Pb. PET 2004 MCQ

If a shell fired from a cannon, explodes in mid air, then

A

Its total kinetic energy increases

B

Its total momentum increases

C

Its total momentum decreases

D

None of these

Question 179: Palette 179/226

Errorless DCE 2004 MCQ

A body is moving with a velocity v, breaks up into two equal parts. One of the part retraces back with velocity v. Then the velocity of the other part is

A

v in forward direction

B

3v in forward direction

C

v in backward direction

D

3v in backward direction

Question 180: Palette 180/226

Errorless CBSE PMT 2004 MCQ

A ball of mass 2kg and another of mass 4kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of

A

$\sqrt{2}:1$

B

1:4

C

1:2

D

$1:\sqrt{2}$

Question 181: Palette 181/226

Errorless KCET 2004 MCQ

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

A

4

B

8

C

6

D

10

Question 182: Palette 182/226

Errorless AIEEE 2004; BHU 2006 MCQ

A body of mass m accelerates uniformly from rest to $v_{1}$ in time $t_{1}$ . As a function of time t, the instantaneous power delivered to the body is

A

$\frac{mv_{1}t}{t_{1}}$

B

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

C

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

D

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

Question 183: Palette 183/226

Errorless UPSEAT 2004 MCQ

Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of 0.4 m/s. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is

A

0.4m/s

B

0.2m/s

C

0.1m/s

D

0.05m/s

Question 184: Palette 184/226

Errorless DCE 2004 MCQ

Two balls at same temperature collide. What is conserved

A

Temperature

B

Velocity

C

Kinetic energy

D

Momentum

Question 185: Palette 185/226

Errorless BCECE 2004; J & K CET 2006 MCQ

A body of mass M moves with velocity v and collides elastically with a another body of mass m (M>>m) at rest then the velocity of body of mass m is

A

v

B

2v

C

v/2

D

Zero

Question 186: Palette 186/226

Errorless IIT-JEE (Screening) 2004; J & K CET 2006 MCQ

A particle is placed at the origin and a force $F = kx$ is acting on it (where $k$ is 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 187: Palette 187/226

Errorless MP PET 2003 MCQ

A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10 N is acting on it in a direction making an angle of $60^{\circ}$ with the x-axis and displaces it along the x-axis by 4 metres. The work done by the force is

A

2.5 J

B

7.25 J

C

40 J

D

20 J

Question 188: Palette 188/226

Errorless MP PET 2003 MCQ

The potential energy of a weight less spring compressed by a distance $a$ is proportional to

A

$a$

B

$a^2$

C

$a^{-2}$

D

$a^0$

Question 189: Palette 189/226

Errorless CBSE PMT 2003; KCET 2012 MCQ

A stationary particle explodes into two particles of a masses $m_{1}$ and $m_{2}$ which move in opposite directions with velocities $v_{1}$ and $v_{2}$ . The ratio of their kinetic energies $E_{1}/E_{2}$ is

A

$m_{1}/m_{2}$

B

1

C

$m_{1}v_{2}/m_{2}v_{1}$

D

$m_{2}/m_{1}$

Question 190: Palette 190/226

Errorless IIT-JEE (Screening) 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 191: Palette 191/226

Errorless MP PMT 2003 MCQ

A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then

A

Lorry will come to rest in a shorter distance

B

Car will come to rest in a shorter distance

C

Both come to rest in a same distance

D

None of the above

Question 192: Palette 192/226

Errorless AIEEE 2003 MCQ

Consider the following two statements 1 Linear momentum of a system of particles is zero 2 Kinetic energy of a system of particles is zero, Then

A

1 implies 2 and 2 implies 1

B

1 does not imply 2 and 2 does not imply 1

C

1 implies 2 but 2 does not imply 1

D

1 does not imply 2 but 2 implies 1

Question 193: Palette 193/226

Errorless MP PMT 2002; CBSE PMT 2003, 06; UPSEAT 2004; Odisha PMT 2004; WB-JEE 2012 MCQ

If a long spring is stretched by 0.02 m, its potential energy is U. If the spring is stretched by 0.1 m, then its potential energy will be

A

$\frac{U}{5}$

B

U

C

5U

D

25U

Question 194: Palette 194/226

Errorless Pb. PMT 2002; J & K CET 2004 MCQ

A body moving with velocity v has momentum and kinetic energy numerically equal. What is the value of v

A

2m/s

B

$\sqrt{2}$ m/s

C

1m/s

D

0.2 m/s

Question 195: Palette 195/226

Errorless AIEEE 2002; DCE 2002; BCECE 2006; WB-JEE 2012 MCQ

If a body looses half of its velocity on penetrating $3\mathrm{cm}$ in a wooden block, then how much will it penetrate more before coming to rest

A

$1\mathrm{cm}$

B

$2\mathrm{cm}$

C

$3\mathrm{cm}$

D

$4\mathrm{cm}$

Question 196: Palette 196/226

Errorless Kerala PET 2002; CBSE PMT (Mains) 2010 MCQ

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is

A

$\frac{MV^{2}}{T}$

B

$\frac{1}{2}\frac{MV^{2}}{T^{2}}$

C

$\frac{MV^{2}}{T^{2}}$

D

$\frac{1}{2}\frac{MV^{2}}{T}$

Question 197: Palette 197/226

Errorless Kerala PET 2002; EAMCET 2009 MCQ

A body of mass 2kg makes an elastic collision with another body at rest and continues to move in the original direction with one fourth of its original speed. The mass of the second body which collides with the first body is

A

2 kg

B

1.2 kg

C

3 kg

D

1.5 kg

Question 198: Palette 198/226

Errorless Kerala PMT 2002; MP PET 2002; WB-JEE 2013 MCQ

A bullet of mass m moving with velocity v strikes a block of mass M at rest and gets embedded into it. The kinetic energy of the composite block will be

A

$\frac{1}{2}mv^{2}\times\frac{m}{(m+M)}$

B

$\frac{1}{2}mv^{2}\times\frac{M}{(m+M)}$

C

$\frac{1}{2}mv^{2}\times\frac{(M+m)}{M}$

D

$\frac{1}{2}Mv^{2}\times\frac{m}{(m+M)}$

Question 199: Palette 199/226

Errorless IIT-JEE (Screening) 2002; DCE 2006 MCQ

A particle which is constrained to move along the $x$ -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 constants. For $x \geq 0$ , the functional from of the potential energy $U(x)$ of the particle is

A

B

C

D

Question 200: Palette 200/226

Errorless MP PMT 2001; CBSE PMT 2004 MCQ

A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is

A

0.01 m

B

0.1 m

C

0.2 m

D

0.5 m

Question 201: Palette 201/226

Errorless BCECE 2001; CBSE PMT 2007; AIIMS 2008; Kerala PET 2011 MCQ

A vertical spring with force constant K is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is

A

$mg(h + d) + \frac{1}{2} Kd^2$

B

$mg(h + d) - \frac{1}{2} Kd^2$

C

$mg(h - d) - \frac{1}{2} Kd^2$

D

$mg(h - d) + \frac{1}{2} Kd^2$

Question 202: Palette 202/226

Errorless Kerala (Engg.) 2001; EAMCET 2001; DPMT 2004; UP CPMT 2006 MCQ

A truck of mass 30,000kg moves up an inclined plane of slope 1 in 100 at a speed of 30 kmph. The power of the truck is (Given $g = 10ms^{-2}$ )

A

25 kW

B

10 kW

C

5 kW

D

2.5 kW

Question 203: Palette 203/226

Errorless UPSEAT 2001; EAMCET 2009 MCQ

A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly each after with a velocity of $12m/s$ , then the velocity of the third part which has 3 times mass of each part is

A

$4\sqrt{2} m/s$ at an angle of $45^{\circ}$ from each body

B

$24\sqrt{2} m/s$ at an angle of $135^{\circ}$ from each body

C

$6\sqrt{2} m/s$ at $135^{\circ}$ from each body

D

$4\sqrt{2} m/s$ at $135^{\circ}$ from each body

Question 204: Palette 204/226

Errorless DCE 2001, 02; Odisha JEE 2002 MCQ

A body of mass $M_{1}$ collides elastically with another mass $M_{2}$ at rest. There is maximum transfer of energy when

A

$M_{1} > M_{2}$

B

$M_{1} < M_{2}$

C

$M_{1} = M_{2}$

D

Same for all values of $M_{1}$ and $M_{2}$

Question 205: Palette 205/226

Errorless UPSEAT 2000; CPMT 2002; Pb. PET 2004; MP PMT 2012 MCQ

The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be

A

30

B

40

C

10

D

20

Question 206: Palette 206/226

Errorless MHCET 2000; Kerala PMT 2008; AMU PMT 2009; AIPMT (Cancelled) 2015 MCQ

Two similar springs P and Q have spring constants $K_{P}$ and $K_{Q}$ , such that $K_{P} > K_{Q}$ . They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs $W_{P}$ and $W_{Q}$ are related as, in case (a) and case (b), respectively

A

$W_{P} = W_{Q}; W_{P} = W_{Q}$

B

$W_{P} > W_{Q}; W_{Q} > W_{P}$

C

$W_{P} < W_{Q}; W_{Q} < W_{P}$

D

$W_{P} = W_{Q}; W_{P} > W_{Q}$

Question 207: Palette 207/226

Errorless DPMT 2000; Odisha JEE 2005 MCQ

A mass of 100g strikes the wall with speed 5m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 \times 10^{-3}$ sec, what is the force applied on the mass by the wall

A

$250\sqrt{3}$ N to right

B

250 N to right

C

$250\sqrt{3}$ N to left

D

250 N to left

Question 208: Palette 208/226

Errorless IIT-JEE 1999; UPSEAT 2003 MCQ

A particle free to move along the $x$ -axis has potential energy given by $U(x) = k$ $[1 - \exp (-x)^2]$ for $-\infty \leq x \leq +\infty$ , where $k$ is a positive constant of appropriate dimensions. Then

A

At point away from the origin, the particle is in unstable equilibrium

B

For any finite non-zero value of $x$ , there is a force directed away from the origin

C

If its total mechanical energy is $k / 2$ , it has its minimum kinetic energy at the origin

D

For small displacements from x=0, the motion is simple harmonic

Question 209: Palette 209/226

Errorless CBSE PMT 1998; Kerala PET 2012 MCQ

A force acts on a 30 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 metres and t is in seconds. The work done during the first 4 seconds is

A

5.28 J

B

450 mJ

C

490 mJ

D

530 mJ

Question 210: Palette 210/226

Errorless AIIMS 1998; UPSEAT 2000; JIPMER 2001; Kerala PMT 2004 MCQ

A light and a heavy body have equal momenta. Which one has greater K.E

A

The light body

B

The heavy body

C

The K.E. are equal

D

Data is incomplete

Question 211: Palette 211/226

Errorless AIIMS 1998, 2002; KCET 2000; CPMT 2003; J & K CET 2004; Kerala PMT 2005; RPMT 2006 MCQ

If the K.E. of a particle is doubled, then its momentum will

A

Remain unchanged

B

Be doubled

C

Be quadrupled

D

Increase $\sqrt{2}$ times

Question 212: Palette 212/226

Errorless AFMC 1998; RPMT 1999; DPMT 2000; MP PET 2004 MCQ

The kinetic energy of a body of mass 3 kg and momentum 2 Ns is

A

1 J

B

$\frac{2}{3} J$

C

$\frac{3}{2} J$

D

4 J

Question 213: Palette 213/226

Errorless BHU 1998; JIPMER 2001, 02; BHU 2005; AFMC 2005 MCQ

Which of the following is not a perfectly inelastic collision

A

Striking of two glass balls

B

A bullet striking a bag of sand

C

An electron captured by a proton

D

A man jumping onto a moving cart

Question 214: Palette 214/226

Errorless JIPMER 1997; CBSE PMT 1999; BHU 2000; RPMT 2000; Odisha JEE 2002 MCQ

A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joules, the angle which the force makes with the direction of motion of the body is

A

0°

B

30°

C

60°

D

90°

Question 215: Palette 215/226

Errorless BHU 1997; MP PET 2000; CBSE PMT 2000; MH CET 2000; JIPMER 2001, 02; AMU (Med.) 2002; DPMT 2003 MCQ

The power of a pump, which can pump 200kg of water to a height of 200m in 10sec is $(g=10m/s^{2})$

A

40 kW

B

80 kW

C

400 kW

D

960 kW

Question 216: Palette 216/226

Errorless MP PMT 1997; CBSE PMT 1998; AIIMS 2000; UPSEAT 2001; MP PET 2001, 02, 07; Kerala PMT 2008 MCQ

Two equal masses $m_{1}$ and $m_{2}$ moving along the same straight line with velocities + 3 m/s and - 5 m/s respectively collide elastically. Their velocities after the collision will be respectively

A

+4m/s for both

B

-3 m/s and +5 m/s

C

-4 m/s and +4 m/s

D

$-5m / s$ and $+3m / s$

Question 217: Palette 217/226

Errorless CPMT 1997; MP PET 1999; DPMT 1999, 2005; JIPMER 2000 MCQ

A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity

A

v/2

B

2v

C

$\dfrac{v}{\sqrt{2}}$

D

v

Question 218: Palette 218/226

Errorless BHU 1997; J & K CET 2010; CBSE PMT (Pre.) 2011 MCQ

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m

A

13 J

B

18 J

C

21 J

D

26 J

Question 219: Palette 219/226

Errorless AFMC 1996, 2006; BHU 2001; DCE 2004, 09; AIIMS 2006; UP CPMT 2006 MCQ

In an inelastic collision, what is conserved

A

Kinetic energy

B

Momentum

C

Both a) and b)

D

Neither a) nor b)

Question 220: Palette 220/226

Errorless CBSE PMT 1996; MP PMT/PET 1998; AIIMS 1999; JIPMER 2001, 02; RPMT 2005 MCQ

A particle of mass m moving with velocity v strikes a stationary particle of mass 2m and sticks to it. The speed of the system will be

A

v/2

B

2v

C

v/3

D

3v

Question 221: Palette 221/226

Errorless Manipal MEE 1995; AIEEE 2002, 06; Pb. PET 2004; CBSE PMT 2005; KCET 2007; Odisha JEE 2008 MCQ

A bomb of mass 9kg explodes into 2 pieces of mass 3kg and 6kg. The velocity of mass 3kg is 1.6 m/s, the K.E. of mass 6kg is

A

3.84 J

B

9.6 J

C

1.92 J

D

2.92 J

Question 222: Palette 222/226

Errorless EAMCET (Engg.) 1995; WB-JEE 2009 MCQ

Two bodies of masses 2m and m have their K.E. in the ratio 8:1, then their ratio of momenta is

A

1:1

B

2:1

C

4:1

D

8:1

Question 223: Palette 223/226

Errorless CBSE PMT 1995; AIEEE 2003 MCQ

A ${}^{238}U$ nucleus decays by emitting an alpha particle of speed $v\ ms^{-1}$ . The recoil speed of the residual nucleus is (in $ms^{-1}$ )

A

-4v / 234

B

v / 4

C

-4v / 238

D

4v / 238

Question 224: Palette 224/226

Errorless BHU 1995; MP PET 1996; AMU (Med.) 1999; JIPMER 2000 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

$t^{1/2}$

B

$t^{3/4}$

C

$t^{3/2}$

D

$t^2$

Question 225: Palette 225/226

Errorless MCQ

A body of mass $(5 \pm 0.5)$ kg is moving with a velocity of $(20 \pm 0.4)$ m/s. Its kinetic energy will be

A

$(1000 \pm 140)J$

B

$(1000 \pm 0.14)J$

C

$(500 \pm 0.14)J$

D

$(500 \pm 140)J$

Question 226: Palette 226/226

Errorless MCQ

A force $F$ acting on an object varies with distance $x$ as shown here. The force is in newton and $x$ in metre. The work done by the force in moving the object from $x = 0$ to $x = 6 m$

A

$4.5 J$

B

$13.5 J$

C

$9.0 J$

D

$18.0 J$