Question 1: Palette 1/121

Objective NEET 2019 MCQ

A force $F = 20 + 10y$ acts on a particle in y-direction, where F is in newton and y is in metre. Work done by this force to move the particle from y = 0 to y = 1m is

A

5 J

B

25 J

C

20 J

D

30 J

Question 2: Palette 2/121

Objective NEET 2019 MCQ

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes $(L + l)$ . The elastic potential energy stored in the extended wire is

A

MgL

B

$\frac{1}{2}Mgl$

C

$\frac{1}{2}MgL$

D

MgL

Question 3: Palette 3/121

Objective NEET (Odisha) 2019 MCQ

An object of mass 500 g, initially at rest acted upon by a variable force whose x component varies with x in the manner shown in figure. The velocities of the object at points x = 8 m and x = 12 m, would be the respective values of (nearly)

A

$18\mathrm{ms}^{-1}$ and $24.4\mathrm{ms}^{-1}$

B

$23\mathrm{ms}^{-1}$ and $24.4\mathrm{ms}^{-1}$

C

$23\mathrm{ms}^{-1}$ and $20.6\mathrm{ms}^{-1}$

D

$18\mathrm{ms}^{-1}$ and $20.6\mathrm{ms}^{-1}$

Question 4: Palette 4/121

Objective AIIMS 2019 MCQ

Initially spring in its natural length. Now, a block of mass 0.25 kg is released, then find out the value of maximum force by system on the floor.

A

$15\mathrm{N}$

B

$20\mathrm{N}$

C

$25\mathrm{N}$

D

$30\mathrm{N}$

Question 5: Palette 5/121

Objective JIPMER 2019 MCQ

The rate of decrease of kinetic energy is $9.6 \, Js^{-1}$ . Find the magnitude of force acting on particle when its speed is $3 \, ms^{-1}$ .

A

3.2 N

B

4.8 N

C

2.4 N

D

5.6 N

Question 6: Palette 6/121

Objective JIPMER 2018 MCQ

If a machine perform 4000 J output work and 1000 J is inside loss due to friction, then find the efficiency.

A

80%

B

30%

C

25%

D

60%

Question 7: Palette 7/121

Objective JIPMER 2018 MCQ

Kinetic energy of a particle is increased by 4 times. What will be the relation between initial and final momentum?

A

$p_2 = 2p_1$

B

$p_2 = p_1 / 2$

C

$p_2 = p_1$

D

$p_2 = 4p_1$

Question 8: Palette 8/121

Objective JIPMER 2018 MCQ

1000 N force is required to lift a hook and 10000 N force is requires to lift a load slowly. Find power required to lift hook with load with speed $v = 0.5 \, ms^{-1}$ .

A

5 kW

B

1.5 kW

C

5.5 kW

D

4.5 kW

Question 9: Palette 9/121

Objective NEET 2017 MCQ

A spring of force constant k is cut into lengths of ratio 1:2:3. They are connected in series and the new force constant is $k'$ . If they are connected in parallel and force constant is $k''$ , then $k':k''$ is

A

1:6

B

1:9

C

1:11

D

1:14

Question 10: Palette 10/121

Objective AIIMS 2017 MCQ

A force $\mathbf{F} = -k(y\hat{\mathbf{i}} + x\hat{\mathbf{j}})$ , 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 11: Palette 11/121

Objective AIIMS 2017 MCQ

Assertion A spring of force constant k is cut into two pieces having lengths in the ratio 1:2. The force constant of series combination of the two parts is 3k/2. Reason The spring connected in series are represented by $k = k_{1} + k_{2}$ .

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 12: Palette 12/121

Objective AIIMS 2017 MCQ

The figure shows a mass m on a frictionless surface. It is connected to rigid wall by the mean of a massless spring of its constant k. Initially, the spring is at its natural position. If a force of constant magnitude starts acting on the block towards right, then the speed of the block when the deformation in spring is x, will be

A

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

B

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

C

$\sqrt {\frac {x (F - k)}{m}}$

D

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

Question 13: Palette 13/121

Objective AIIMS 2017 MCQ

A person of weight 70 kg wants to loose 7 kg by going up and down 12m high stairs. Assume he burns twice as much fat while going up than going down. If 1 kg of fat is burnt on expending 9000 k-cal. How many times must he go up and down to reduce his 7 kg weight?(Take, $g=10\ ms^{-2}$ )

A

$18\times 10^{3}$ times

B

$24\times 10^{3}$ times

C

$30\times 10^{3}$ times

D

$21\times 10^{3}$ times

Question 14: Palette 14/121

Objective JIPMER 2017 MCQ

A skier starts from rest at point $A$ and slides down the hill without turning or breaking. The friction coefficient is $\mu$ . When he stops at point $B$ , his horizontal displacement is $s$ . What is the height difference between points $A$ and $B$ ? (The velocity of the skier is small, so that the additional pressure on the snow due to the curvature can be neglected. Neglect also the friction of air and the dependence of $\mu$ on the velocity of the skier.)

A

$h = \mu s$

B

$h = \frac{\mu}{s}$

C

$h = 2\mu s$

D

$h = \mu s^2$

Question 15: Palette 15/121

Objective NEET 2016 MCQ

A body of mass 1 kg begins to move under the action of a time dependent force $\mathbf{F} = (2t \hat{\mathbf{i}} + 3t^{2} \hat{\mathbf{j}})$ N, where $\hat{i}$ and $\hat{j}$ are unit vectors along X and Y-axis. What power will be developed by the force at the time (t)?

A

$(2t^{2} + 4t^{4})$ W

B

$(2t^{3} + 3t^{4})$ W

C

$(2t^{3} + 3t^{5})$ W

D

$(2t + 3t^{3})$ W

Question 16: Palette 16/121

Objective NEET 2016 MCQ

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to $8 \times 10^{-4}$ J by the end of the second revolution after the beginning of the motion?

A

$0.15 \, ms^{-2}$

B

$0.18 \, ms^{-2}$

C

$0.2 \, ms^{-2}$

D

$0.1 \, ms^{-2}$

Question 17: Palette 17/121

Objective CBSE AIPMT 2015 MCQ

A block of mass 10 kg moving in x-direction with a constant speed of $10 \, ms^{-1}$ , is subjected to a retarding force $F = -0.1 \, x \, Jm^{-1}$ during its travel from x = 20 m to 30 m. Its final KE will be

A

475 J

B

450 J

C

275 J

D

250 J

Question 18: Palette 18/121

Objective CBSE AIPMT 2015 MCQ

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest, the force on the particle at time t is

A

$\sqrt{\frac{mk}{2}} t^{-1/2}$

B

$\sqrt{mk} t^{-1/2}$

C

$\sqrt{2mk} t^{-1/2}$

D

$\frac{1}{2}\sqrt{mk} t^{-1/2}$

Question 19: Palette 19/121

Objective AIIMS 2015, UK PMT 2015 MCQ

A force $F = (10 + 0.5x)$ acts on a particle in the x-direction. What would be the work done by this force during a displacement from x = 0 to x = 2m (F is in newton and x in metre)

A

31.5 J

B

63 J

C

21 J

D

42 J

Question 20: Palette 20/121

Objective UK PMT 2015 MCQ

A block of mass m=11.7 kg is to be pushed a distance of s=4.65 m along an incline and raised to a distance of h=2.86 m. Assuming frictionless surface, calculate the work done in applying a force parallel to the incline to push the block up at a constant speed. (Take, $g=9.8\ ms^{-2}$ )

A

$328\mathrm{J}$

B

$656\mathrm{J}$

C

$164\mathrm{J}$

D

$530\mathrm{J}$

Question 21: Palette 21/121

Objective CGPMT 2015, UK PMT 2015 MCQ

An elevator weighing 500 kg is to be lifted up at a constant velocity of $0.20 \, ms^{-1}$ . What would be the minimum horse power of the motor to be used?

A

10.30 hp

B

5.15 hp

C

2.62 hp

D

1.31 hp

Question 22: Palette 22/121

Objective Kerala CEE 2015 MCQ

Two bodies of different masses are moving with same kinetic energy. Then, the ratio of their momenta is equal to the ratio of their

A

masses

B

square of masses

C

square root of masses

D

cube root of masses

Question 23: Palette 23/121

Objective Kerala CEE 2015 MCQ

Two bodies of masses 1 kg and 2 kg moving with same velocities are stopped by the same force. Then, the ratio of their stopping distances is

A

1:2

B

2:1

C

$\sqrt{2}$ :1

D

$1:\sqrt{2}$

Question 24: Palette 24/121

Objective Manipal 2015 MCQ

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

A

$\frac{mvit}{t_{1}}$

B

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

C

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

D

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

Question 25: Palette 25/121

Objective EAMCET 2015 MCQ

A uniform chain of length l is placed on a smooth horizontal table, such that half of its length hangs over one edge. It is released from rest, the velocity with which it leaves the table is

A

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

B

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

C

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

D

$\sqrt{\frac{gl}{3}}$

Question 26: Palette 26/121

Objective KCET 2015 MCQ

The kinetic energy of a body of mass 4 kg and momentum 6 N-s will be

A

4.5 J

B

2.5 J

C

5.5 J

D

3.5 J

Question 27: Palette 27/121

Objective UK PMT 2015 MCQ

A body of mass m = 3.90 kg slides on a horizontal frictionless table with a speed of $v = 1.20 \, ms^{-1}$ . It is brought to rest in compressing a spring in its path. How much does spring is compressed, if its force constant k is $135 \, Nm^{-1}$ ?

A

0.204 m

B

0.408 m

C

0.804 m

D

4.04 m

Question 28: Palette 28/121

Objective MHT CET 2014 MCQ

A string of length L and force constant k is stretched to obtain extension l. It is further stretched to obtain extension $l_{1}$ . The work done in second stretching is

A

$\frac{1}{2}kl_{1}(2l+l_{1})$

B

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

C

$\frac{1}{2}k(l^{2}+l_{1}^{2})$

D

$\frac{1}{2}k(l_{1}^{2}-l^{2})$

Question 29: Palette 29/121

Objective Uttarakhand PMT 2014 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 30: Palette 30/121

Objective Kerala CEE 2014 MCQ

If two persons A and B take 2 s and 4 s respectively to lift an object to the same height h, then the ratio of their powers is

A

1:2

B

1:1

C

2:1

D

1:3

E

3:1

Question 31: Palette 31/121

Objective Kerala CEE 2014 MCQ

If a machine gun fires n bullets per second each with kinetic energy K, then the power of the machine gun is

A

$nK^{2}$

B

$\frac{K}{n}$

C

$n^{2}K$

D

nK

E

$\frac{n}{K}$

Question 32: Palette 32/121

Objective NEET 2013 MCQ

A uniform force of $(3\hat{\mathbf{i}}+\hat{\mathbf{j}})$ N acts on a particle of mass 2 kg. Hence, the particle is displaced from position $(2\hat{\mathbf{i}}+\hat{\mathbf{k}})$ m to position $(4\hat{\mathbf{i}}+3\hat{\mathbf{j}}-\hat{\mathbf{k}})$ m. The work done by the force on the particle is

A

9 J

B

6 J

C

13 J

D

15 J

Question 33: Palette 33/121

Objective J&K CET 2013 MCQ

The power (P) of an engine lifting a mass of 100 kg upto a height of 10 m in 1 min is

A

163.3 W

B

9800 W

C

10000 W

D

5000 W

Question 34: Palette 34/121

Objective EAMCET 2013 MCQ

A body of mass 300 kg is moved through 10 m along a smooth inclined plane of angle $30^{\circ}$ . The work done in moving (in joules) is (Take, $g = 9.8 \, ms^{-2}$ )

A

4900

B

9800

C

14700

D

2450

Question 35: Palette 35/121

Objective EAMCET 2013 MCQ

Force constants of two wires A and B of the same material are k and 2k, respectively. If the two wires are stretched equally, then the ratio of work done in stretching $\left(\frac{W_{A}}{W_{B}}\right)$ is

A

$\frac{1}{3}$

B

$\frac{1}{2}$

C

$\frac{3}{2}$

D

$\frac{1}{4}$

Question 36: Palette 36/121

Objective KCET 2013 MCQ

A truck accelerates from speed v to 2v. Work done during this is

A

three times as the work done in accelerating it from rest to v

B

same as the work done in accelerating it from rest to v

C

four times as the work done in accelerating it from rest to v

D

less than the work done in accelerating it from rest to v

Question 37: Palette 37/121

Objective Kerala CET 2013 MCQ

A block of 200 g mass is dropped from a height of 2 m on to a spring and compresses the spring to a distance of 50 cm. The force constant of the spring is

A

$20 \, Nm^{-1}$

B

$40 \, Nm^{-1}$

C

$30 \, Nm^{-1}$

D

$60 \, Nm^{-1}$

E

$10 \, Nm^{-1}$

Question 38: Palette 38/121

Objective CBSE AIPMT 2012 MCQ

The potential energy of a particle in a force field is $U = \frac{A}{r^{2}} - \frac{B}{r}$ , where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is

A

B/2A

B

2A/B

C

A/B

D

B/A

Question 39: Palette 39/121

Objective AIIMS 2012 MCQ

The particle of mass 50 kg is at rest. The work done to accelerate it by 20 ms $^{-1}$ in 10 s is

A

$10^{3}$ J

B

$10^{4}$ J

C

$2 \times 10^{3}$ J

D

$4 \times 10^{4}$ J

Question 40: Palette 40/121

Objective BCECE Mains 2012 MCQ

The slope of kinetic energy and displacement curve for a particle in motion will be

A

equal to the acceleration of the particle

B

directly proportional to the acceleration of the particle

C

inversely proportional to the acceleration of the particle

D

None of the above

Question 41: Palette 41/121

Objective BHU 2012 MCQ

Two masses m and 2m are attached to two ends of an ideal spring as shown in figure. When the spring is in the compressed state, the energy of the spring is 60 J, if the spring is released, then at its natural length,

A

energy of smaller body will be 20 J

B

energy of smaller body will be 40 J

C

energy of smaller body will be 10 J

D

energy of both the bodies will be same

Question 42: Palette 42/121

Objective 2000 MCQ

A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is [NCERT Exemplar]

A

+ 2000 J

B

- 200 J

C

zero

D

- 20000 J

Question 43: Palette 43/121

Objective MCQ

A body is falling freely under the action of gravity alone in vacuum. Which of the following quantities remain constant during the fall? [NCERT Exemplar]

A

Kinetic energy

B

Potential energy

C

Total mechanical energy

D

Total linear momentum

Question 44: Palette 44/121

Objective MCQ

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because [NCERT Exemplar]

A

the two magnetic forces are equal and opposite, so they produce no net effect

B

the magnetic forces do not work on each particle

C

the magnetic forces do equal and opposite (but non-zero) work on each particle

D

the magnetic forces are necessarily negligible

Question 45: Palette 45/121

Objective MCQ

An engine exerts a force $\mathbf{F} = (20\hat{\mathbf{i}} - 3\hat{\mathbf{j}} + 5\hat{\mathbf{k}})$ N and moves with velocity $\mathbf{v} = (6\hat{\mathbf{i}} + 20\hat{\mathbf{j}} - 3\hat{\mathbf{k}})$ ms $^{-1}$ . The power of the engine (in watt) is

A

45

B

75

C

20

D

10

Question 46: Palette 46/121

Objective MCQ

A rod of mass m and length l is lying on a horizontal table. Work done in making it stand on one end will be

A

mgl

B

$\frac{mgl}{2}$

C

$\frac{mgl}{4}$

D

2mgl

Question 47: Palette 47/121

Objective MCQ

The pointer reading versus load graph for a spring balance is as shown in the figure. The spring constant is

A

15 kgf/cm

B

5 kgf/cm

C

0.1 kgf/cm

D

10 kgf/cm

Question 48: Palette 48/121

Objective MCQ

A body of mass m was slowly pulled up the hill by a force F which at each point was directed along the tangent of the trajectory. All surfaces are smooth. Find the work performed by this force.

A

mgl

B

- mgl

C

mgh

D

zero

Question 49: Palette 49/121

Objective 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 50: Palette 50/121

Objective MCQ

If v, p and E denote velocity, linear momentum and kinetic energy of the particle respectively, then

A

$p = \frac{dE}{dv}$

B

$p = \frac{dE}{dt}$

C

$p = \frac{dv}{dt}$

D

$p = \frac{dE}{dv} \times \frac{dE}{dt}$

Question 51: Palette 51/121

Objective MCQ

The energy required to accelerate a car from rest to $10 \, ms^{-1}$ is W. The energy required to accelerate the car from $10 \, ms^{-1}$ to $20 \, ms^{-1}$ is

A

W

B

2 W

C

3 W

D

4 W

Question 52: Palette 52/121

Objective MCQ

Which of the following diagrams most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit? [NCERT Exemplar]

A

B

C

D

Question 53: Palette 53/121

Objective MCQ

A particle is moved from $(0,0)$ to $(a,a)$ under a force $\mathbf{F} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}})$ from two paths. Path 1 is OP and path 2 is OQP. Let $W_{1}$ and $W_{2}$ be the work done by this force in 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 54: Palette 54/121

Objective MCQ

A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x?

A

B

C

D

Question 55: Palette 55/121

Objective MCQ

Which of the following diagrams represents variation of total mechanical energy of a pendulum oscillating in air as function of time? [NCERT Exemplar]

A

B

C

D

Question 56: Palette 56/121

Objective MCQ

An object of mass m, initially at rest under the action of a constant force F attains a velocity v in time t. Then, the average power supplied to mass is

A

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

B

$\frac{Fv}{2}$

C

Both a) and b)

D

None of these

Question 57: Palette 57/121

Objective MCQ

A particle at rest on a frictionless table is acted upon by a horizontal force which is constant in magnitude and direction. A graph is plotted for the work done on the particle W against the speed of the particle v. If there are no frictional forces acting on the particle, the graph will look like

A

B

C

D

Question 58: Palette 58/121

Objective MCQ

A car moving with a speed of $40 \, kmh^{-1}$ can be stopped by applying brakes in 2 m. If the car is moving with a speed of $80 \, kmh^{-1}$ , the minimum stopping distance under similar brakes will be

A

8 m

B

2 m

C

4 m

D

6 m

Question 59: Palette 59/121

Objective MCQ

A long spring is stretched by 2 cm. Its potential energy is U. If the spring is stretched by 10 cm, its potential energy would be

A

$\frac{U}{25}$

B

$\frac{U}{5}$

C

5U

D

25U

Question 60: Palette 60/121

Objective MCQ

A body is falling under gravity. When it loses a gravitational potential energy by U, its speed is v. The mass of the body will be

A

$\frac{2U}{v}$

B

$\frac{U}{2v}$

C

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

D

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

Question 61: Palette 61/121

Objective MCQ

How much mass is converted into energy per day in Tarapur nuclear power plant operated at $10^{7}$ kW?

A

9.6 g

B

9.63 kg

C

8.6 g

D

7 g

Question 62: Palette 62/121

Objective MCQ

A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments: one in which the charged particle is also a proton and in another a positron. In the same time t, the work done on the two moving charged particles is [NCERT Exemplar]

A

same as the same force law is involved in the two experiments

B

less for the case of a positron, as the positron moves away more rapidly and the force on it weakens

C

more for the case of a positron, as the positron moves away a larger distance

D

same as the work done by charged particle on the stationary proton

Question 63: Palette 63/121

Objective MCQ

The potential energy function for a particle executing linear SHM is given by $V(x) = \frac{1}{2} kx^{2}$ where, k is the force constant of the oscillator (see figure). For $k = 0.5 Nm^{-1}$ , the graph of $V(x)$ versus x is shown in the figure. A particle of total energy E turns back when it reaches $x = \pm x_{m}$ . If V and K indicate the PE and KE respectively of the particle at $x = +x_{m}$ , then which of the following is correct? [NCERT Exemplar]

A

V = 0, K = E

B

V = E, K = 0

C

V < E, K = 0

D

V = 0, K < E

Question 64: Palette 64/121

Objective MCQ

The potential energy between the atoms in a molecule is given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^{6}}$ where, a and b are positive constants and x is the distance between the atoms. The atom is in equilibrium when

A

x = 0

B

$x = \left(\frac{a}{2b}\right)^{1/6}$

C

$x = \left(\frac{2a}{b}\right)^{1/6}$

D

$x = \left(\frac{11a}{5b}\right)^{1/6}$

Question 65: Palette 65/121

Objective MCQ

A ball is thrown vertically upwards with a velocity of $10 \, ms^{-1}$ . It returns to the ground with a velocity of $9 \, ms^{-1}$ . If $g = 9.8 \, ms^{-2}$ , then the maximum height attained by the ball is nearly (assume air resistance to be uniform)

A

5.1 m

B

4.1 m

C

4.61 m

D

5 m

Question 66: Palette 66/121

Objective MCQ

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

A

at x = 1.16 m

B

at x = 2 m

C

at bottom of plane

D

at x = 2.5 m

Question 67: Palette 67/121

Objective MCQ

A mass-spring system oscillates such that the mass moves on a rough surface having coefficient of friction $\mu$ . It is compressed by a distance a from its normal length and on being released, it moves to a distance b from its equilibrium position. The decrease in amplitude for one half-cycle (-a to b) is

A

$\frac{\mu mg}{k}$

B

$\frac{2\mu mg}{k}$

C

$\frac{\mu g}{k}$

D

$\frac{k}{\mu mg}$

Question 68: Palette 68/121

Objective MCQ

A block of mass 5 kg slides down a rough inclined surface. The angle of inclination is $45^{\circ}$ . The coefficient of sliding friction is 0.20. When the block slides 10 cm, the work done on the block by force of friction is

A

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

B

1J

C

$-\sqrt{2}J$

D

-1J

Question 69: Palette 69/121

Objective MCQ

The system shown in the figure is released from rest. At the instant when mass M has fallen through a distance h, the velocity of m will be

A

$\sqrt{2gh}$

B

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

C

$\sqrt{\frac{2gh(M - m)}{m + M}}$

D

$\sqrt{\frac{2gh(M + m)}{m - M}}$

Question 70: Palette 70/121

Objective MCQ

The curved portions are smooth and horizontal surface is rough. The block is released from P. At what distance from A, it will stop (if $\mu = 0.2$ )?

A

$1\mathrm{m}$

B

$2\mathrm{m}$

C

$3\mathrm{m}$

D

$4\mathrm{m}$

Question 71: Palette 71/121

Objective MCQ

A particle moves on a rough horizontal ground with some initial velocity, say $v_{0}$ . If $\left(\frac{3}{4}\right)$ th of its kinetic energy is lost due to friction in time $t_{0}$ , then coefficient of friction between the particle and the ground is

A

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

B

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

C

$\frac{3v_{0}}{4gt_{0}}$

D

$\frac{v_{0}}{gt_{0}}$

Question 72: Palette 72/121

Objective MCQ

If a body of mass 200 g falls from a height 200 m and its total potential energy is converted into kinetic energy at the point of contact of the body with the surface, then decrease in potential energy of the body at the contact is (Take, $g = 10 \, ms^{-2}$ )

A

900 J

B

600 J

C

400 J

D

200 J

Question 73: Palette 73/121

Objective MCQ

A stone of mass 2 kg is projected upwards with kinetic energy of 98 J. The height at which the kinetic energy of the body becomes half of its original value will be (Take, $g = 9.8ms^{-2}$ )

A

5 m

B

2.5 m

C

1.5 m

D

0.5 m

Question 74: Palette 74/121

Objective MCQ

A toy gun uses a spring of very large value of force constant k. When charged before being triggered in the upward direction, the spring is compressed by a small distance x. If mass of shot is m, on being triggered, it will go up to a height of

A

$\frac{kx^{2}}{mg}$

B

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

C

$\frac{kx^{2}}{2mg}$

D

$\frac{(kx)^{2}}{mg}$

Question 75: Palette 75/121

Objective MCQ

Water falling from a 50 m high fall is to be used for generating electrical energy. If $1.8 \times 10^{5}$ kg of water falls per hour and half the gravitational potential energy can be converted into electrical energy, how many 100 W bulb can be lit?

A

50

B

125

C

150

D

200

Question 76: Palette 76/121

Objective MCQ

Given that the displacement of the body (in metre) is a function of time as follows $x = 2t^{4} + 5$ The mass of the body is 2 kg. What is the increase in its kinetic energy one second after the start of motion?

A

8 J

B

16 J

C

32 J

D

64 J

Question 77: Palette 77/121

Objective MCQ

An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angle $\theta$ with the vertical. Work done by the force F is

A

mgL (1 - sin $\theta$ )

B

mgL

C

mgL (1 - cos $\theta$ )

D

mgL (1 + cos $\theta$ )

Question 78: Palette 78/121

Objective 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

(1/2)d

Question 79: Palette 79/121

Objective MCQ

Kinetic energy of a particle moving in a straight line varies with time t as $K = 4t^{2}$ . The force acting on the particle

A

is constant

B

is increasing

C

is decreasing

D

first increases and then decreases

Question 80: Palette 80/121

Objective MCQ

Three particles A, B and C are projected from the top of a tower with the same speed. A is thrown straight upwards, B straight down and C horizontally. They hit the ground with speeds $v_{A}$ , $v_{B}$ and $v_{C}$ , then which of the following is correct?

A

$v_{A} = v_{B} > v_{C}$

B

$v_{A} = v_{B} = v_{C}$

C

$v_{A} > v_{B} = v_{C}$

D

$v_{B} > v_{C} > v_{A}$

Question 81: Palette 81/121

Objective MCQ

A particle is moving in a conservative force field from point A to point B. $U_{A}$ and $U_{B}$ are the potential energies of the particle at points A and B; and $W_{C}$ is the work done by conservative forces in the process of taking the particle from A and B. Which of the following is true?

A

$W_{C} = U_{B} - U_{A}$

B

$W_{C} = U_{A} - U_{B}$

C

$U_{A} > U_{B}$

D

$U_{B} > U_{A}$

Question 82: Palette 82/121

Objective MCQ

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

A

$1 \, ms^{-1}$

B

$4 \, ms^{-1}$

C

$2 \, ms^{-1}$

D

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

Question 83: Palette 83/121

Objective MCQ

An open knife edge of mass m is dropped from a height h on a wooden floor. If the blade penetrates up to the depth d into the wood, the average resistance offered by the wood to the knife edge is

A

$mg\left(1+\frac{h}{d}\right)$

B

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

C

$mg\left(1-\frac{h}{d}\right)$

D

$mg\left(1+\frac{d}{h}\right)$

Question 84: Palette 84/121

Objective MCQ

If v be the instantaneous velocity of the body dropped from the top of a tower, when it is located at height h, then which of the following remains constant?

A

$gh + v^{2}$

B

$gh + \frac{v^{2}}{2}$

C

$gh - \frac{v^{2}}{2}$

D

$gh - v^{2}$

Question 85: Palette 85/121

Objective MCQ

A block of mass 1 kg slides down a rough inclined plane of inclination $60^{\circ}$ starting from its top. If coefficient of kinetic friction is 0.5 and length of the plane d = 2 m, then work done against friction is

A

2.45 J

B

4.9 J

C

9.8 J

D

19.6 J

Question 86: Palette 86/121

Objective MCQ

A raindrop falling from a height h above ground, attains a near terminal velocity when it has fallen through a height $(3/4)h$ . Which of the diagrams shown in figure correctly shows the change in kinetic and potential energy of the drop during its fall up to the ground? [NCERT Exemplar]

A

B

C

D

Question 87: Palette 87/121

Objective MCQ

In a shotput event, an athlete throws the shotput of mass 10 kg with an initial speed of $1 \, ms^{-1}$ at $45^{\circ}$ from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be $10 \, ms^{-2}$ , the kinetic energy of the shotput when it just reaches the ground will be

A

2.5 J

B

5 J

C

52.5 J

D

155 J

Question 88: Palette 88/121

Objective MCQ

A block of mass m is attached to two unstretched springs of spring constants k, each as shown. The block is displaced towards right through a distance x and is released. The speed of the block as it passes through the mean position will be

A

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

B

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

C

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

D

$x\frac{2k}{m}$

Question 89: Palette 89/121

Objective MCQ

A particle of mass 1 g executes an oscillatory motion on the concave surface of a spherical dish of radius 2m placed on a horizontal plane. If the motion of the particle begins from a point on the dish at a height of 1 cm from the horizontal plane, the total distance covered by the particle before it comes to rest, is (Curved surface is smooth and $\mu = 0.01$ for horizontal surface)

A

2 cm

B

10 cm

C

1 cm

D

20 cm

Question 90: Palette 90/121

Objective MCQ

The net work done by the tension in the figure when the bigger block of mass M touches the ground is

A

$+Mgd$

B

$-(M + m)gd$

C

$-mgd$

D

zero

Question 91: Palette 91/121

Objective MCQ

A block $A$ of mass $M$ rests on a wedge $B$ of mass $2M$ and inclination $\theta$ . There is sufficient friction between $A$ and $B$ , so that $A$ does not slip on $B$ . If there is no friction between $B$ and ground, the compression in spring is

A

$\frac{Mg\cos\theta}{k}$

B

$\frac{Mg\cos\theta\sin\theta}{k}$

C

$\frac{Mg\sin\theta}{k}$

D

zero

Question 92: Palette 92/121

Objective MCQ

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half the length, the line OA will

A

shift towards F-axis

B

shift towards X-axis

C

remain as it is

D

become double in length

Question 93: Palette 93/121

Objective MCQ

A motor drives a body along a straight line with a constant force. The power P developed by the motor must vary with time t as

A

B

C

D

Question 94: Palette 94/121

Objective MCQ

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

A

$s^{2/3}$

B

$s^{-5/3}$

C

$s^{1/2}$

D

$s^{0}$

Question 95: Palette 95/121

Objective MCQ

The force acting on a body moving along X-axis varies with the position of the particle as shown in the figure. The body 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 96: Palette 96/121

Objective MCQ

A body of mass 0.5 kg travels in a straight line with velocity $v = a x^{3/2}$ , where $a = 5 m^{-1/2} s^{-1}$ . The work done by the net force during its displacement from x = 0 to x = 2 m is [NCERT Exemplar]

A

1.5 J

B

50 J

C

10 J

D

100 J

Question 97: Palette 97/121

Objective MCQ

The figure shows a particle sliding on a frictionless track, which terminates in a straight horizontal section. If the particle starts slipping from the point A, how far away from the track will the particle hit the ground?

A

1m

B

2m

C

3m

D

4m

Question 98: Palette 98/121

Objective MCQ

A uniform chain has a mass M and length L. It is placed on a frictionless table with length $l_{0}$ hanging over the edge. The chain begins to slide down. Then, the speed v with which the end slides down from the edge is given by

A

$v = \sqrt{\frac{g}{L}(L + l_{0})}$

B

$v = \sqrt{\frac{g}{L}(L - l_{0})}$

C

$v = \sqrt{\frac{g}{L}(L^{2} - l_{0}^{2})}$

D

$v = \sqrt{2g(L - l_{0})}$

Question 99: Palette 99/121

Objective MCQ

A bead of mass 1/2 kg starts from rest from A to B move in a vertical plane along a smooth fixed quarter ring of radius 5 m, under the action of a constant horizontal force F = 5 N as shown in figure. The speed of bead as it reaches the point B is (Take, $g = 10 \, ms^{-2}$ )

A

$14.14\mathrm{ms}^{-1}$

B

$7.07\mathrm{ms}^{-1}$

C

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

D

$25\mathrm{ms}^{-1}$

Question 100: Palette 100/121

Objective MCQ

A car of mass m is accelerating on a level smooth road under the action of a single force F. The power delivered to the car is constant and equal to P. If the velocity of the car at an instant is v, then after travelling how much distance will it become double?

A

$\frac{7mv^3}{3P}$

B

$\frac{4mv^3}{3P}$

C

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

D

$\frac{18mv^3}{7P}$

Question 101: Palette 101/121

Objective MCQ

A particle is released from a height $H$ . At certain height, its kinetic energy is two times its potential energy. Height and speed of particle at that instant are

A

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

B

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

C

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

D

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

Question 102: Palette 102/121

Objective MCQ

A force of $F = 0.5 \, \text{N}$ is applied on lower block as shown in figure . The work done by lower block on upper block for a displacement of $3 \, \text{m}$ of the upper block with respect to ground is (Take, $g = 10 \, \text{ms}^{-2}$ )

A

$-0.5\mathrm{J}$

B

$0.5\mathrm{J}$

C

$2\mathrm{J}$

D

$-2\mathrm{J}$

Question 103: Palette 103/121

Objective MCQ

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the following diagrams shown in figure correctly represents the displacement-time curve for its motion? [NCERT Exemplar]

A

B

C

D

Question 104: Palette 104/121

Objective MCQ

A small block of mass m is kept on a rough inclined surface of inclination $\theta$ fixed in an elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in a time t will be

A

zero

B

$mgvt \cos^{2} \theta$

C

$mgvt \sin^{2} \theta$

D

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

Question 105: Palette 105/121

Objective MCQ

A pendulum of mass 1 kg and length l = 1m is released from rest at angle $\theta = 60^{\circ}$ . The power delivered by all the forces acting on the bob at angle $\theta = 30^{\circ}$ will be (Take, $g = 10 \, ms^{-2}$ )

A

13.5 W

B

20.4 W

C

24.6 W

D

zero

Question 106: Palette 106/121

Objective MCQ

A uniform flexible chain of mass m and length l 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

$\sqrt{\frac{gl}{2}}$

B

$\sqrt{gl}$

C

$\sqrt{2gl}$

D

$\sqrt{3gl}$

Question 107: Palette 107/121

Objective MCQ

The potential energy of a particle of mass 1 kg is $U = 10 + (x - 2)^{2}$ . Here, U is in joule and x in metre on the positive X-axis. Particle travels up to $x = +6 \, m$ . Choose the correct option.

A

On negative $X$ -axis, particle travels up to $x = -2\mathrm{m}$

B

The maximum kinetic energy of the particle is 16 J

C

Both a) and b) are correct

D

Both a) and b) are incorrect

Question 108: Palette 108/121

Objective MCQ

A plank of mass 10 kg and a block of mass 2 kg are placed on a horizontal plane as shown in the figure. There is no friction between plane and plank. The coefficient of friction between block and plank is 0.5. A force of 60 N is applied on plank horizontally. In first 2 s, the work done by friction on the block is

A

−100 J

B

100 J

C

zero

D

200 j

Question 109: Palette 109/121

Objective MCQ

A block of mass m is pulled along a horizontal surface by applying a force at an angle $\theta$ with the horizontal. If the block travels with a uniform velocity and has a displacement d and the coefficient of friction is $\mu$ , then the work done by the applied force is

A

$\frac{\mu mgd}{\cos\theta + \mu \sin\theta}$

B

$\frac{\mu mgd\cos\theta}{\cos\theta + \mu\sin\theta}$

C

$\frac{\mu mgd \sin\theta}{\cos\theta + \mu \sin\theta}$

D

$\frac{\mu mgd\cos\theta}{\cos\theta - \mu\sin\theta}$

Question 110: Palette 110/121

Objective MCQ

An ideal massless spring S can be compressed 1 m by a force of 100 N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at $30^{\circ}$ to the horizontal. A 10 kg block M is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by 2 m. If $g = 10 \, ms^{-2}$ , what is the speed of mass just before it touches the spring?

A

$\sqrt{20}\ \mathrm{m\,s^{-1}}$

B

$\sqrt{30}\ \mathrm{m\,s^{-1}}$

C

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

D

$\sqrt{40}\ \mathrm{m\,s^{-1}}$

Question 111: Palette 111/121

Objective MCQ

Assertion At stable equilibrium position of a body, kinetic energy cannot be zero. Because it is maximum. Reason During oscillations of a body, potential energy is minimum at stable equilibrium position.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 112: Palette 112/121

Objective MCQ

Assertion If work done by conservative force is negative, then potential energy associated with that force should increase. Reason This is according to the relation, $\Delta U = -W$ . Here, $\Delta U$ is change in potential energy and W is work done by conservative force.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 113: Palette 113/121

Objective MCQ

Assertion If the surface between the blocks A and B is rough, then work done by friction on block B is always negative. Reason Total work done by friction in both the blocks is always zero.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 114: Palette 114/121

Objective MCQ

Assertion Force applied on a block moving in one dimension is producing a constant power, then the motion should be uniformly accelerated. Reason This constant power multiplied with time is equal to the change in kinetic energy.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 115: Palette 115/121

Objective MCQ

Assertion Total work done by spring may be positive, negative or zero. Reason Direction of spring force is always towards mean position.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 116: Palette 116/121

Objective MCQ

Assertion At any instant, the magnitude of rate of change of potential energy of the projectile of mass 1 kg is numerically equal to magnitude of $a \cdot v$ (where, a is acceleration due to gravity and v is velocity at that instant) Reason The graph representing power delivered by the gravitational force acting on the projectile with time will be straight line with negative slope.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 117: Palette 117/121

Objective MCQ

Mark out the correct statement(s).

A

Total work done by internal forces on a system is always zero.

B

Total work done by internal forces on a system may sometimes be zero.

C

Total work done by friction can never be zero.

D

Total work done by friction is always zero.

Question 118: Palette 118/121

Objective MCQ

Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in figure. [NCERT Exemplar] Which of the following statement(s) is/are correct?

A

Both the stones reach the bottom at the same time but not with the same speed.

B

Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.

C

Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.

D

Both the stones reach the bottom at different times and with different speeds.

Question 119: Palette 119/121

Objective MCQ

In position A, kinetic energy of a particle is 60 J and potential energy is -20 J. In position B, kinetic energy is 100 J and potential energy is 40 J. Choose the correct statement, if the particle moves from A to B.

A

Work done by conservative forces is 50 J.

B

Work done by external forces is 40 J.

C

Net work done by all the forces is 40 J.

D

Net work done by all the forces is 100 J.

Question 120: Palette 120/121

Objective MCQ

Which of the following statement(s) is/are correct? I. Spring force is a conservative force. II. Potential energy is defined only for conservative forces.

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Question 121: Palette 121/121

Objective MCQ

Which of the following statement(s) is/are correct? I. If momentum of a body increases by 50%, its kinetic energy will increase by 125%. II. Kinetic energy is proportional to square of velocity.

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II