Question 1: Palette 1/135

Objective NEET 2020 MCQ

Two bodies of masses 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity g is

A

$g / 2$

B

$g / 5$

C

$g / 10$

D

$g$

Question 2: Palette 2/135

Objective NEET 2020 MCQ

Calculate the acceleration of the block and trolley system shown in the figure. The coefficient of kinetic friction between the trolley and the surface is 0.05 ( $g = 10 \, m/s^{2}$ , mass of the string is negligible and no other friction exists).

A

$1.25\mathrm{m / s}^2$

B

$1.50\mathrm{m / s}^2$

C

$1.66\mathrm{m / s}^2$

D

$1.00\mathrm{m / s}^2$

Question 3: Palette 3/135

Objective NEET (Odisha) 2019 MCQ

A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck, suddenly moves to the right with an acceleration of a. The pendulum will tilt

A

to the left and the angle of inclination of the pendulum with the vertical is $\sin^{-1}\left(\frac{g}{a}\right)$

B

to the left and angle of inclination of the pendulum with the vertical is $\tan^{-1}\left(\frac{a}{g}\right)$

C

to the left and angle of inclination of the pendulum with the vertical is $\sin^{-1}\left(\frac{a}{g}\right)$

D

to the left and angle of inclination of the pendulum with the vertical is $\tan^{-1}\left(\frac{g}{a}\right)$

Question 4: Palette 4/135

Objective NEET (Odisha) 2019 MCQ

A body of mass m is kept on a rough horizontal surface (coefficient of friction = $\mu$ ). Horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given F, where F is

A

$|F| = mg + \mu mg$

B

$|F| = \mu mg$

C

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

D

$|F| = mg$

Question 5: Palette 5/135

Objective NEET 2019 MCQ

A particle moving with velocity v is acted by three forces shown by the vector triangle PQR. The velocity of the particle will

A

decrease

B

remain constant

C

change according to the smallest force $QR$

D

increase

Question 6: Palette 6/135

Objective AIIMS 2019 MCQ

Assertion: A glass ball is dropped on concrete floor can easily get broken compared, if it is dropped on wooden floor. Reason: On concrete floor, glass ball will take less time to come to rest.

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 7: Palette 7/135

Objective AIIMS 2019 MCQ

A gun applies a force F on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t)$ N. The bullet emerges out with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero.

A

0.2 N-s

B

0.3 N-s

C

0.1 N-s

D

0.4 N-s

Question 8: Palette 8/135

Objective AIIMS 2019 MCQ

Assertion: Even though net external force on a body is zero, momentum need not to conserved. Reason: The internal interaction between particles of a body cancels out momentum of each other.

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 9: Palette 9/135

Objective NEET 2018 MCQ

A block of mass m is placed on a smooth inclined wedge ABC of inclination $\theta$ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and $\theta$ for the block to remain stationary on the wedge is

A

$a = g\cos \theta$

B

$a = \frac{g}{\sin\theta}$

C

$a = \frac{g}{\csc\theta}$

D

$a = g\tan \theta$

Question 10: Palette 10/135

Objective NEET 2018 MCQ

Which one of the following statements is incorrect?

A

Frictional force opposes the relative motion.

B

Limiting value of static friction is directly proportional to normal reaction.

C

Rolling friction is smaller than sliding friction.

D

Coefficient of sliding friction has dimensions of length.

Question 11: Palette 11/135

Objective AIIMS 2018 MCQ

In the figure, mass of a ball is $\frac{9}{5}$ times mass of the rod. Length of rod is 1 m. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod.

A

$1.4\mathrm{s}$

B

$2.45\mathrm{s}$

C

$3.25\mathrm{s}$

D

$5\mathrm{s}$

Question 12: Palette 12/135

Objective AIIMS 2018 MCQ

Assertion: Angle of repose is equal to angle of limiting friction. Reason: When a body is just at the point of motion, the force of friction of this stage is called as limiting friction.

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 13: Palette 13/135

Objective AIIMS 2018 MCQ

A wooden wedge of mass M and inclination angle $\alpha$ rest on a smooth floor. A block of mass m is kept on wedge. A force F is applied on the wedge as shown in the figure, such that block remains stationary with respect to wedge. The magnitude of force $F$ is

A

$(M + m)g\tan \alpha$

B

$g\tan \alpha$

C

$mg\cos \alpha$

D

$(M + m)g\operatorname {cosec}\alpha$

Question 14: Palette 14/135

Objective AIIMS 2018 MCQ

A piece of ice slides down a rough inclined plane at $45^{\circ}$ inclination in twice the time that it takes to slide down an identical but frictionless inclined plane. What is the coefficient of friction between ice and incline?

A

$\frac{3}{7\cot\theta}$

B

$\frac{4}{7\cot\theta}$

C

$\frac{3}{4\cot\theta}$

D

$\frac{7}{9\cot\theta}$

Question 15: Palette 15/135

Objective AIIMS 2018 MCQ

A body of mass 5 kg is suspended by a spring balance on an inclined plane as shown in figure. So, force applied on spring balance is

A

50 N

B

25 N

C

500 N

D

10 N

Question 16: Palette 16/135

Objective JIPMER 2018 MCQ

A force of 10N acts on a body of mass 0.5 kg for 0.25s starting from rest. What is its impulse?

A

0.25 N-s

B

2.5 N-s

C

0.5 N-s

D

0.75 N-s

Question 17: Palette 17/135

Objective JIPMER 2018 MCQ

A mass M is hung with a light inextensible string as shown in the figure. Find the tension of the horizontal string.

A

$\sqrt{2} Mg$

B

$\sqrt{3} Mg$

C

$2Mg$

D

$3Mg$

Question 18: Palette 18/135

Objective NEET 2017 MCQ

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively

A

g, g/3

B

g/3, g

C

g, g

D

g/3, g/3

Question 19: Palette 19/135

Objective AIIMS 2017 MCQ

Four blocks of same mass connected by strings are pulled by a force F on a smooth horizontal surface as shown in figure. The tension $T_{1}, T_{2}$ and $T_{3}$ will be

A

$T_{1} = \frac{1}{4} F, T_{2} = \frac{3}{2} F, T_{3} = \frac{1}{4} F$

B

$T_{1} = \frac{1}{4} F, T_{2} = \frac{1}{2} F, T_{3} = \frac{1}{2} F$

C

$T_{1} = \frac{3}{4} F, T_{2} = \frac{1}{2} F, T_{3} = \frac{1}{4} F$

D

$T_{1} = \frac{3}{4} F, T_{2} = \frac{1}{2} F, T_{3} = \frac{1}{2} F$

Question 20: Palette 20/135

Objective AIIMS 2017 MCQ

A body of mass $5 \times 10^{-3}$ kg is launched upon a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. Obtain the coefficient of friction between the body and the plane, if the time of ascent is half of the time of descent.

A

0.346

B

0.921

C

1.926

D

2.912

Question 21: Palette 21/135

Objective JIPMER 2017 MCQ

A long block A of mass M is at rest on a smooth horizontal surface. A small block B of mass M/2 is placed on A at one end and projected along A with some velocity v. The coefficient of friction between the block is $\mu$ . Then, the accelerations of blocks A and B before reaching a common velocity will be respectively

A

$\frac{\mu g}{2}$ (towards right), $\frac{\mu g}{2}$ (towards left)

B

$\mu g$ (towards right), $\mu g$ (towards left)

C

$\frac{\mu g}{2}$ (towards right), $\mu g$ (towards left)

D

$\mu g$ (towards right), $\frac{\mu g}{2}$ (towards left)

Question 22: Palette 22/135

Objective JIPMER 2017 MCQ

A box of mass 8 kg is placed on a rough inclined plane of inclination $30^{\circ}$ . Its downward motion can be prevented by applying a horizontal force F, then value of F for which friction between the block and the incline surface is minimum, is

A

$\frac{80}{\sqrt{3}}$ N

B

$40\sqrt{3}$ N

C

$\frac{40}{\sqrt{3}}$ N

D

$80\sqrt{3}$ N

Question 23: Palette 23/135

Objective JIPMER 2017 MCQ

Two masses 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown in figure, the 10 kg mass has acceleration of $12 \, m/s^{2}$ . The value of acceleration of 20 kg mass is

A

4 $m/s^2$

B

10 $m/s^2$

C

20 $m/s^2$

D

30 $m/s^2$

Question 24: Palette 24/135

Objective JIPMER 2017, NEET 2013 MCQ

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and the lower half of the plane is given by

A

$\mu = 2 \tan \theta$

B

$\mu = \tan \theta$

C

$\mu = 2 / (\tan \theta)$

D

$\mu = 1 / \tan \theta$

Question 25: Palette 25/135

Objective NEET 2016 MCQ

A rigid ball of mass m strikes a rigid wall at $60^{\circ}$ and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be

A

mv

B

2 mv

C

mv/2

D

mv/3

Question 26: Palette 26/135

Objective AIIMS 2015 MCQ

A body of mass 40 kg resting on rough horizontal surface is subjected to a force P which is just enough to start the motion of the body. If $\mu_{s}=0.5$ , $\mu_{k}=0.4$ , $g=10\ ms^{-2}$ and the force P is continuously applied on the body, then the acceleration of the body is

A

zero

B

$1\ ms^{-2}$

C

$2\ ms^{-2}$

D

$24\ ms^{-2}$

Question 27: Palette 27/135

Objective EAMCET 2015 MCQ

A balloon of mass 10 kg is raising up with an acceleration of $20 \, ms^{-2}$ . If a mass of 4 kg is removed from the balloon, its acceleration becomes (Take, $g = 10 \, ms^{-2}$ )

A

$40 \, ms^{-2}$

B

$20 \, ms^{-2}$

C

$30 \, ms^{-2}$

D

$12 \, ms^{-2}$

Question 28: Palette 28/135

Objective WB JEE 2015 MCQ

Block B lying on a table weighs w. The coefficient of static friction between the block and the table is $\mu$ . Assume that the cord between B and the knot is horizontal. The maximum weight of the block A for which the system will be stationary is

A

$\frac{w\tan\theta}{\mu}$

B

$\mu w\tan\theta$

C

$\mu w\sqrt{1+\tan^2\theta}$

D

$\mu w\sin\theta$

Question 29: Palette 29/135

Objective CBSE AIPMT 2015 MCQ

Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively are in contact on a frictionless surface as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is

A

$2\mathrm{N}$

B

$6\mathrm{N}$

C

$8\mathrm{N}$

D

$18\mathrm{N}$

Question 30: Palette 30/135

Objective CBSE AIPMT 2015 MCQ

A block $A$ of mass $m_{1}$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end, another block $B$ of mass $m_{2}$ is suspended. The coefficient of kinetic friction between the block and the table is $\mu_{k}$ . When the block $A$ is sliding on the table, the tension in the string is

A

$\frac{(m_2 + \mu_k m_1) g}{(m_1 + m_2)}$

B

$\frac{(m_2 - \mu_k m_1) g}{(m_1 + m_2)}$

C

$\frac{m_1 m_2 (1 + \mu_k) g}{(m_1 + m_2)}$

D

$\frac{m_1 m_2 (1 - \mu_k) g}{(m_1 + m_2)}$

Question 31: Palette 31/135

Objective CBSE AIPMT 2014 MCQ

A balloon with mass m is descending down with an acceleration a (where, a < g). How much mass should be removed from it, so that it starts moving up with an acceleration a?

A

$\frac{2ma}{g + a}$

B

$\frac{2ma}{g - a}$

C

$\frac{ma}{g + a}$

D

$\frac{ma}{g - a}$

Question 32: Palette 32/135

Objective EAMCET 2014 MCQ

A bullet moving with a velocity of $30\sqrt{2}$ ms $^{-1}$ is fired into a fixed target. It penetrated into the target to the extent of s metre. If the same bullet is fired into a target of thickness $\frac{s}{2}$ metres and of the same material with the same velocity, then the bullet comes out of the target with velocity, is

A

$20 \, ms^{-1}$

B

$30 \, ms^{-1}$

C

$20\sqrt{2} \, ms^{-1}$

D

$10\sqrt{2} \, ms^{-1}$

Question 33: Palette 33/135

Objective CBSE AIPMT 2014 MCQ

A system consists of three masses $m_{1}$ , $m_{2}$ and $m_{3}$ connected by a string passing over a pulley P. The mass $m_{1}$ hangs freely and $m_{2}$ and $m_{3}$ are on a rough horizontal table (the coefficient of friction $= \mu$ ). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_{1}$ is (Assume, $m_{1} = m_{2} = m_{3} = m$ )

A

$\frac{g(1 - g\mu)}{9}$

B

$\frac{2g\mu}{3}$

C

$\frac{g(1 - 2\mu)}{3}$

D

$\frac{g(1 - 2\mu)}{2}$

Question 34: Palette 34/135

Objective MHT CET 2014 MCQ

A wooden block of mass 8 kg slides down an inclined plane of inclination $30^{\circ}$ to the horizontal with constant acceleration $0.4 \, ms^{-2}$ . The force of friction between the block and inclined plane is (Take, $g = 10 \, ms^{-2}$ )

A

12.2 N

B

24.4 N

C

36.8 N

D

48.8 N

Question 35: Palette 35/135

Objective WB JEE 2014 MCQ

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at $45^{\circ}$ and the block is released from rest. The block takes a time t in moving a distance d. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time t/2 in moving down the same distance d. The coefficient of friction is

A

3/4

B

5/4

C

1/2

D

$1/\sqrt{2}$

Question 36: Palette 36/135

Objective KCET 2014 MCQ

A body of mass m is placed on a rough surface with coefficient of friction $\mu$ inclined at $\theta$ . If the mass is in equilibrium, then

A

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

B

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

C

$\theta = \tan^{-1} \frac{m}{\mu}$

D

$\theta = \tan^{-1} \frac{\mu}{m}$

Question 37: Palette 37/135

Objective NEET 2013 MCQ

Three blocks with masses m, 2m and 3m are connected by strings as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity)

A

Zero

B

2 mg

C

3 mg

D

6 mg

Question 38: Palette 38/135

Objective EAMCET 2013 MCQ

A balloon starting from rest ascends vertically with uniform acceleration to a height of 100 m in 10 s. The force on the bottom of the balloon by a mass of 50 kg is (Take, $g = 10 \, ms^{-2}$ )

A

100 N

B

300 N

C

600 N

D

400 N

Question 39: Palette 39/135

Objective EAMCET 2013 MCQ

A 3 kg block is placed over a 10 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the blocks is 0.2. If a horizontal force of 20 N is applied to 3 kg block, accelerations of the two blocks (in ms $^{-2}$ ) are (Take, $g = 10 \, ms^{-2}$ )

A

$\frac{13}{4}, 0.6$

B

$\frac{14}{4}, 3$

C

$\frac{13}{4}, 3$

D

$\frac{14}{3}, 0.6$

Question 40: Palette 40/135

Objective Kerala CEE 2013 MCQ

A 60 kg person is weighed by a balance as 54 kg in a lift which is accelerated downwards. The acceleration of the lift is

A

$1.26 \, ms^{-2}$

B

$1.76 \, ms^{-2}$

C

$1.98 \, ms^{-2}$

D

$0.98 \, ms^{-2}$

E

None of these

Question 41: Palette 41/135

Objective UP CPMT 2013 MCQ

A lift starting from rest with a constant upward acceleration moves 1.5 m in 0.4 s. If a person standing in the lift holds a packet of 2 kg by a string, then the tension in the string due to motion is

A

5.89 N

B

57.1 N

C

67.1 N

D

None of these

Question 42: Palette 42/135

Objective AIIMS 2012 MCQ

A body of mass 0.25 kg is projected with muzzle velocity $100 \, ms^{-1}$ from a tank of mass 100 kg. What is the recoil velocity of the tank?

A

$5 \, ms^{-1}$

B

$25 \, ms^{-1}$

C

$0.5 \, ms^{-1}$

D

$0.25 \, ms^{-1}$

Question 43: Palette 43/135

Objective AIIMS 2012 MCQ

A rocket with a lift-off mass $3.5 \times 10^{4}$ kg is blast upward with an initial acceleration of $10 \, ms^{-2}$ . Then, the initial thrust of the blast is

A

$1.75 \times 10^{5} \, N$

B

$3.5 \times 10^{5} \, N$

C

$7 \times 10^{5} \, N$

D

$14 \times 10^{5} \, N$

Question 44: Palette 44/135

Objective AIIMS 2012 MCQ

A marble block of mass 2 kg lying on ice when given a velocity of $6 \, ms^{-1}$ is stopped by friction in 10 s. Then, the coefficient of friction is

A

0.01

B

0.02

C

0.03

D

0.06

Question 45: Palette 45/135

Objective BHU 2012 MCQ

A 40 kg slab rests on a frictionless floor. A 10 kg block rests on the top of the slab as shown in figure. The static coefficient of friction between the block and the slab is 0.60 while the kinetic coefficient is 0.40. The 10 kg block is acted upon by a horizontal force of 100 N. If $g = 9.8 \, ms^{-2}$ , the resulting acceleration of the slab will be

A

$61 \, ms^{-2}$

B

$152 \, ms^{-2}$

C

$147 \, ms^{-2}$

D

$0.98 \, ms^{-2}$

Question 46: Palette 46/135

Objective BCECE 2012 MCQ

An inclined plane of height h and length l have the angle of inclination $\theta$ . The time taken by a body to come from the top to the bottom of this inclined plane will be

A

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

B

$\frac{1}{\sin\theta}\sqrt{\frac{2h}{g}}$

C

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

D

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

Question 47: Palette 47/135

Objective BCECE (Mains) 2012 MCQ

If a coin is dropped in a lift it takes $t_{1}$ time to reach the floor and takes $t_{2}$ time when lift is moving up with constant acceleration, then which one of the following relation is correct?

A

$t_{1} = t_{2}$

B

$t_{1} > t_{2}$

C

$t_{2} > t_{1}$

D

$t_{1} >> t_{2}$

Question 48: Palette 48/135

Objective BCECE (Mains) 2012 MCQ

A 60 kg mass is pushed with a enough force to start it moving and the same force is continued to act afterwards. If the coefficient of static friction and sliding friction are 0.5 and 0.4 respectively, then the acceleration of the body will be

A

$1 \, ms^{-2}$

B

$3.9 \, ms^{-2}$

C

$4.9 \, ms^{-2}$

D

$6 \, ms^{-2}$

Question 49: Palette 49/135

Objective AFMC 2012 MCQ

A body is hanging from a rigid support by an inextensible string of length l. It is struck inelastically by an identical body of mass m with horizontal velocity $v = \sqrt{2gl}$ , the tension in the string increases just after striking by

A

mg

B

3 mg

C

2 mg

D

None of these

Question 50: Palette 50/135

Objective AFMC 2012 MCQ

A block A of mass 100 kg rests on another block B of mass 200 kg and is tied to a wall as shown in the figure. The coefficient of friction between A and B is 0.2 and that between B and the ground is 0.3. The minimum force F required to move the block B is (Take, $g = 10 \, ms^{-2}$ )

A

$900\mathrm{N}$

B

$200\mathrm{N}$

C

$1100\mathrm{N}$

D

$700\mathrm{N}$

Question 51: Palette 51/135

Objective AFMC 2012 MCQ

A machine gun fires a bullet of mass 40 g with a velocity $1200 \, ms^{-1}$ . The man holding it can exert a maximum force of 144 N on the gun. How many bullets can be fired per second at the most?

A

Only one

B

Three

C

Can fire any number of bullets

D

$144 \times 48$

Question 52: Palette 52/135

Objective JCECE 2012 MCQ

A monkey of mass 25 kg is holding a vertical rope. The rope does not break, if a body of mass 30 kg is suspended from it, but the rope breaks, if the mass of the body suspended with the rope exceeds 30 kg. What will be the maximum acceleration with which the monkey can climb up along the rope? (Take, $g = 10 \, ms^{-2}$ )

A

$2 \, ms^{-2}$

B

$25 \, ms^{-2}$

C

$3 \, ms^{-2}$

D

$4 \, ms^{-2}$

Question 53: Palette 53/135

Objective JCECE 2012 MCQ

A body of weight 50 N placed on a horizontal surface is just moved by a force of 282 N. The frictional force and normal reaction are

A

$2\mathrm{N},3\mathrm{N}$

B

$5\mathrm{N},6\mathrm{N}$

C

$10\mathrm{N},15\mathrm{N}$

D

$20\mathrm{N},30\mathrm{N}$

Question 54: Palette 54/135

Objective RPMT 2011 MCQ

Diwali rocket is ejecting 50 g of gases/s at a velocity of $400 \, ms^{-1}$ . The accelerating force on the rocket will be

A

22 dyne

B

20 N

C

20 dyne

D

100 N

Question 55: Palette 55/135

Objective AMU 2011 MCQ

A rocket of mass 1000 kg is to be projected vertically upwards. The gases are exhausted vertically downwards with velocity $100 \, ms^{-1}$ with respect to the rocket. What is the minimum rate of burning of fuel, so as to just lift the rocket upwards against the gravitational attraction? (Take, $g = 10 \, ms^{-2}$ )

A

$50 \, kg s^{-1}$

B

$100 \, kg s^{-1}$

C

$200 \, kg s^{-1}$

D

$400 \, kg s^{-1}$

Question 56: Palette 56/135

Objective DUMET 2011 MCQ

In a non-inertial frame, the second law of motion is written as

A

$\mathbf{F} = m\mathbf{a}$

B

$\mathbf{F} = m\mathbf{a} + \mathbf{F}_p$

C

$\mathbf{F} = m\mathbf{a} - \mathbf{F}_p$

D

$\mathbf{F} = 2m\mathbf{a}$ where, $\mathbf{F}_p$ is pseudo force while $\mathbf{a}$ is the acceleration of the body relative to the non-inertial frame.

Question 57: Palette 57/135

Objective AMU 2011 MCQ

A man of mass 60 kg is riding in a lift. The weight of the man when the lift is accelerating upwards and downwards at $2 \, ms^{-2}$ are respectively (Take, $g = 10 \, ms^{-2}$ )

A

720 N and 480 N

B

480 N and 720 N

C

600 N and 600 N

D

None of these

Question 58: Palette 58/135

Objective DUMET 2011 MCQ

An object is moving on a plane surface with uniform velocity $10 \, ms^{-1}$ in presence of a force 10 N. The frictional force between the object and the surface is

A

1 N

B

- 10 N

C

10 N

D

100 N

Question 59: Palette 59/135

Objective MCQ

A metre scale is moving with uniform velocity. This implies

A

the force acting on the scale is zero, but a torque about the centre of mass can act on the scale

B

the force acting on the scale is zero and the torque acting about centre of mass of the scale is also zero

C

the total force acting on it need not be zero but the torque on it is zero

D

Neither the force nor the torque need to be zero

Question 60: Palette 60/135

Objective MCQ

Conservation of momentum in a collision between particles can be understood from

A

conservation of energy

B

Newton's first law only

C

Newton's second law only

D

Both Newton's second and third law

Question 61: Palette 61/135

Objective MCQ

If the elevator in the shown figure is moving upwards with constant acceleration $1 \, ms^{-2}$ , the tension in the string connected to block A of mass 6 kg would be (Take, $g = 10 \, ms^{-2}$ )

A

60 N

B

66 N

C

54 N

D

42 N

Question 62: Palette 62/135

Objective MCQ

A block is placed on the top of a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation a, the block is released. The acceleration of the block relative to the incline is

A

$g \sin \theta$

B

$a \sin \theta$

C

$(g - a) \sin \theta$

D

$(g + a) \sin \theta$

Question 63: Palette 63/135

Objective MCQ

A cricket ball of mass 150 g has an initial velocity $\mathbf{u} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}}) \, \mathrm{ms}^{-1}$ and a final velocity $\mathbf{v} = -(3\hat{\mathbf{i}} + 4\hat{\mathbf{j}}) \, \mathrm{ms}^{-1}$ , after being hit. The change in momentum (final momentum – initial momentum) is (in kg·ms $^{-1}$ )

A

zero

B

$-(0.45\hat{\mathbf{i}} + 0.6\hat{\mathbf{j}})$

C

$-(0.9\hat{\mathbf{i}} + 1.2\hat{\mathbf{j}})$

D

$-5(\hat{\mathbf{i}} + \hat{\mathbf{j}})\hat{\mathbf{i}}$

Question 64: Palette 64/135

Objective MCQ

In the previous question (5), the magnitude of the momentum transferred during the hit is

A

zero

B

$0.75 \, kg \cdot ms^{-1}$

C

$1.5 \, kg \cdot ms^{-1}$

D

$14 \, kg \cdot ms^{-1}$

Question 65: Palette 65/135

Objective MCQ

A block of mass m is placed on a smooth plane inclined at an angle $\theta$ with the horizontal. The force exerted by the plane on the block has a magnitude

A

mg

B

mg sec $\theta$

C

mg cos $\theta$

D

mg sin $\theta$

Question 66: Palette 66/135

Objective MCQ

A block has been placed on an inclined plane. The slope angle $\theta$ of the plane is such that the block slides down the plane at a constant speed. The coefficient of kinetic friction is equal to

A

$\sin\theta$

B

$\cos\theta$

C

g

D

$\tan\theta$

Question 67: Palette 67/135

Objective MCQ

A body is projected up a $45^{\circ}$ rough incline. If the coefficient of friction is 0.5, then the retardation of the block is

A

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

B

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

C

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

D

$\frac{g}{2}$

Question 68: Palette 68/135

Objective MCQ

A rope of length L and mass M is hanging from a rigid support. The tension in the rope at a distance x from the rigid support is

A

Mg

B

$\left(\frac{L-x}{L}\right)Mg$

C

$\left(\frac{L}{L-x}\right)Mg$

D

$\frac{x}{L}Mg$

Question 69: Palette 69/135

Objective MCQ

Consider the shown arrangement. Assume all surfaces to be smooth. If N represents magnitudes of normal reaction between block and wedge, then acceleration of M along horizontal is equal to

A

$\frac{N\sin\theta}{M}$ along + ve $X$ -axis

B

$\frac{N\cos\theta}{M}$ along -ve $X$ -axis

C

$\frac{N\sin\theta}{M}$ along -ve $X$ -axis

D

$\frac{N\sin\theta}{m + M}$ along -ve $X$ -axis

Question 70: Palette 70/135

Objective MCQ

In the above problem, normal reaction between ground and wedge will have magnitude equal to

A

$N \cos \theta + Mg$

B

$N \cos \theta + Mg + mg$

C

$N \cos \theta - Mg$

D

$N \sin \theta + Mg + mg$

Question 71: Palette 71/135

Objective MCQ

A block of mass m is at rest on an inclined plane which is making angle $\theta$ with the horizontal. The coefficient of friction between the block and plane is $\mu$ . Then, frictional force acting between the surfaces is

A

$\mu mg$

B

$\mu mg\sin \theta$

C

$\mu (mg\sin \theta -mg\cos \theta)$

D

$mg\sin \theta$

Question 72: Palette 72/135

Objective MCQ

If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?

A

1cm

B

2 cm

C

3 cm

D

4 cm

Question 73: Palette 73/135

Objective MCQ

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

A

$\cot \alpha = 3$

B

$\tan \alpha = 3$

C

$\sec \alpha = 3$

D

$\csc \alpha = 3$

Question 74: Palette 74/135

Objective MCQ

A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is

A

frictional force along westward

B

muscle force along southward

C

frictional force along south-west

D

muscle force along south-west

Question 75: Palette 75/135

Objective MCQ

A car of mass m starts from rest and acquires a velocity along east $\mathbf{v} = v\hat{\mathbf{i}}(v > 0)$ in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is

A

$\frac{mv}{2}$ eastward and is exerted by the car engine

B

$\frac{mv}{2}$ eastward and is due to the friction on the tyres exerted by the road

C

more than $\frac{mv}{2}$ eastward exerted due to the engine and overcomes the friction of the road

D

$\frac{mv}{2}$ exerted by the engine

Question 76: Palette 76/135

Objective MCQ

In the figure shown, a person wants to raise a block lying on the ground to a height h. In both the cases, if time required is the same, then in which case, he has to exert more force. (Assume pulleys and strings are light) (i) (ii)

A

i

B

ii

C

Same in both

D

Cannot be determined

Question 77: Palette 77/135

Objective MCQ

A body of mass 2kg travels according to the relation $x(t) = pt + qt^{2} + rt^{3}$ , where $q = 4 ms^{-2}$ , $p = 3 ms^{-1}$ and $r = 5 ms^{-3}$ . The force acting on the body at t = 2 s is

A

136 N

B

134 N

C

158 N

D

68 N

Question 78: Palette 78/135

Objective MCQ

A body with mass 5 kg is acted upon by a force $F = (-3\hat{i} + 4\hat{j})$ N. If its initial velocity at t = 0 is $u = (6\hat{i} - 12\hat{j}) \, \text{ms}^{-1}$ , the time at which it will just have a velocity along the Y-axis is

A

zero

B

10 s

C

2 s

D

15 s

Question 79: Palette 79/135

Objective MCQ

A 5000 kg rocket is set for vertical firing. The exhaust speed is $800 \, ms^{-1}$ . To give an initial upward acceleration of $20 \, ms^{-2}$ , the amount of gas ejected per second to supply the needed thrust will be (Take, $g = 10 \, ms^{-2}$ )

A

$127.5 \, kgs^{-1}$

B

$187.5 \, kgs^{-1}$

C

$185.5 \, kgs^{-1}$

D

$137.5 \, kgs^{-1}$

Question 80: Palette 80/135

Objective MCQ

Two blocks are in contact on a frictionless table. One has mass m and the other 2m. A force F is applied on 2m as shown in the figure. Now, the same force F is applied from the right on m. In the two cases, the ratio of force of contact between the two blocks will be

A

same

B

1:2

C

$2:1$

D

$1:3$

Question 81: Palette 81/135

Objective MCQ

A 4 kg block A is placed on the top of 8 kg block B which rests on a smooth table. A just slips on B when a force of 12 N is applied on A. Then, the maximum horizontal force F applied on B to make both A and B move together, is

A

12 N

B

24 N

C

36 N

D

48 N

Question 82: Palette 82/135

Objective MCQ

Find the value of friction forces between the blocks A and B; and between B and ground. (Take, $g=10\ ms^{-2}$ )

A

90 N, 5 N

B

5 N, 90 N

C

5 N, 75 N

D

0 N, 80 N

Question 83: Palette 83/135

Objective MCQ

A block of mass 5 kg is kept on a horizontal floor having coefficient of friction 0.09. Two mutually perpendicular horizontal forces of 3 N and 4 N act on this block. The acceleration of the block is (Take, $g = 10 \, ms^{-2}$ )

A

zero

B

$0.1 \, ms^{-2}$

C

$0.2 \, ms^{-2}$

D

$0.3 \, ms^{-2}$

Question 84: Palette 84/135

Objective MCQ

Two masses A and B of 10 kg and 5 kg respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown in figure. The coefficient of friction of A with the table is 0.2. The minimum mass of C that may be placed on A to prevent it from moving is equal to

A

$15\mathrm{kg}$

B

$10\mathrm{kg}$

C

$5\mathrm{kg}$

D

$20\mathrm{kg}$

Question 85: Palette 85/135

Objective MCQ

In the figure, pulleys are smooth and strings are massless, $m_{1}=1$ kg and $m_{2}=\frac{1}{3}$ kg. To keep $m_{3}$ at rest, mass $m_{3}$ should be

A

1 kg

B

$\frac{2}{3}$ kg

C

$\frac{1}{4}$ kg

D

2 kg

Question 86: Palette 86/135

Objective MCQ

If the coefficient of friction between A and B is $\mu$ , the maximum acceleration of the wedge A for which B will remain at rest with respect to the wedge is

A

$\mu g$

B

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

C

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

D

$\frac{g}{\mu}$

Question 87: Palette 87/135

Objective MCQ

A block of mass 1 kg is at rest relative to a smooth wedge moving leftwards with constant acceleration $a = 5 \, ms^{-2}$ . Let N be the normal reaction between the block and the wedge. Then, (Take, $g = 10 \, ms^{-2}$ )

A

$N = 5\sqrt{5} \, N$

B

N = 15 N

C

$\tan\theta = \frac{1}{3}$

D

$\tan\theta = 2$

Question 88: Palette 88/135

Objective MCQ

A block of mass m is kept on an inclined plane of a lift moving down with acceleration of $2 \, ms^{-2}$ . What should be the coefficient of friction to let the block move down with constant velocity relative to lift?

A

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

B

$\mu = 0.4$

C

$\mu = 0.8$

D

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

Question 89: Palette 89/135

Objective MCQ

Two blocks of mass 5 kg and 3 kg are attached to the ends of a string passing over a smooth pulley fixed to the ceiling of an elevator. The elevator is accelerated upwards. If the acceleration of the blocks is $\frac{9}{32}g$ , the acceleration of the elevator is

A

$\frac{g}{3}$

B

$\frac{g}{4}$

C

$\frac{g}{8}$

D

$\frac{g}{6}$

Question 90: Palette 90/135

Objective MCQ

A balloon of weight w is falling vertically downward with a constant acceleration $a (< g)$ . The magnitude of the air resistance is

A

w

B

$w\left(1+\frac{a}{g}\right)$

C

$w\left(1-\frac{a}{g}\right)$

D

$w\frac{a}{g}$

Question 91: Palette 91/135

Objective MCQ

A smooth inclined plane of length L, having an inclination $\theta$ with horizontal is inside a lift which is moving down with retardation a. The time taken by a block to slide down the inclined plane from rest will be

A

$\sqrt{\frac{2L}{\sqrt{a\sin\theta}}}$

B

$\sqrt{\frac{2L}{g\sin\theta}}$

C

$\sqrt{\frac{2L}{(g - a)\sin\theta}}$

D

$\sqrt{\frac{2L}{(g + a)\sin\theta}}$

Question 92: Palette 92/135

Objective MCQ

A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of $3 \, ms^{-1}$ and $4 \, ms^{-1}$ , respectively. The third piece will be thrown off with a velocity of

A

$1.5 \, ms^{-1}$

B

$2 \, ms^{-1}$

C

$2.5 \, ms^{-1}$

D

$3 \, ms^{-1}$

Question 93: Palette 93/135

Objective MCQ

A wooden box of mass 8 kg slides down an inclined plane of inclination $30^{\circ}$ to the horizontal with a constant acceleration of $0.4 \, ms^{-2}$ . What is the force of friction between the box and inclined plane? (Take, $g = 10 \, ms^{-2}$ )

A

36.8 N

B

76.8 N

C

65.6 N

D

None of these

Question 94: Palette 94/135

Objective MCQ

A mass of 3 kg descending vertically downwards supports a mass of 2 kg by means of a light string passing over a pulley. At the end of 5 s, the string breaks . How much high from now the 2 kg mass will go? (Take, $g = 9.8 \, ms^{-2}$ )

A

4.9 m

B

9.8 m

C

19.6 m

D

2.45 m

Question 95: Palette 95/135

Objective MCQ

The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 m away from the open end ( $\mu = 0.15$ and $g = 10 \, ms^{-2}$ ). The truck starts from rest with an acceleration of $2 \, ms^{-2}$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to

A

4 m

B

8 m

C

16 m

D

32 m

Question 96: Palette 96/135

Objective MCQ

Two blocks of masses $m = 5\mathrm{kg}$ and $M = 10\mathrm{kg}$ are connected by a string passing over a pulley $B$ as shown. Another string connects the centre of pulley $B$ to the floor and passes over another pulley $A$ as shown. An upward force $F$ is applied at the centre of pulley $A$ . Both the pulleys are massless. The accelerations of blocks $m$ and $M$ , if $F$ is $300\mathrm{N}$ are (Take, $g = 10\mathrm{ms}^{-2}$ )

A

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

B

zero, $5\mathrm{ms}^{-2}$ ;

C

zero, zero

D

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

Question 97: Palette 97/135

Objective MCQ

A man of mass m stands on a platform of equal mass m and pulls himself by two ropes passing over pulleys as shown in figure. If he pulls each rope with a force equal to half his weight, his upward acceleration would be

A

$\frac{g}{2}$

B

$\frac{g}{4}$

C

g

D

zero

Question 98: Palette 98/135

Objective MCQ

A 40 N block supported by two ropes. One rope is horizontal and the other makes an angle of $30^{\circ}$ with the ceiling. The tension in the rope attached to the ceiling is approximately

A

80 N

B

40 N

C

$40\sqrt{3}$ N

D

$\frac{40}{\sqrt{3}}$ N

Question 99: Palette 99/135

Objective MCQ

Starting from rest, a body slides down a $45^{\circ}$ inclined plane in twice the time, it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is

A

0.2

B

0.25

C

0.75

D

0.5

Question 100: Palette 100/135

Objective MCQ

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

A

2.5 N

B

0.98 N

C

4.9 N

D

0.49 N

Question 101: Palette 101/135

Objective MCQ

A block of mass m is given an initial downward velocity $v_{0}$ and left on an inclined plane (coefficient of friction=0.6). The block will

A

continue of move down the plane with constant velocity $v_{0}$

B

accelerate downward

C

decelerate and come to rest

D

first accelerate downward then decelerate

Question 102: Palette 102/135

Objective MCQ

Pushing force making an angle $\theta$ to the horizontal is applied on a block of weight $w$ placed on a horizontal table. If the angle of friction is $\phi$ , the magnitude of force required to move the body is equal to

A

$\frac{w \cos \phi}{\cos(\theta - \phi)}$

B

$\frac{w \sin \phi}{\cos(\theta + \phi)}$

C

$\frac{w \tan \phi}{\sin(\theta - \phi)}$

D

$\frac{w \sin \phi}{\tan(\theta - \phi)}$

Question 103: Palette 103/135

Objective MCQ

In the arrangement shown in figure, there is a friction force between the blocks of masses m and 2m kept on a smooth horizontal surface. The mass of the suspended block is m. The block of mass m is stationary with respect to block of mass 2 m. The minimum value of coefficient of friction between m and 2 m is ____

A

$\frac{1}{2}$

B

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

C

$\frac{1}{4}$

D

$\frac{1}{3}$

Question 104: Palette 104/135

Objective MCQ

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

A

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

B

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

C

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

D

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

Question 105: Palette 105/135

Objective MCQ

A man of mass m has fallen into a ditch of width d. Two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Both the friends exert force of equal magnitudes $F$ . exert force of equal magnitudes $F$ . When the man is at a depth $h$ , the value of $F$ is

A

$\frac{mg}{4h}\sqrt{d^2 + 4h^2}$

B

$hmg$

C

$dmg$

D

$\frac{mg}{2h}\sqrt{h^2 + d^2}$

Question 106: Palette 106/135

Objective MCQ

Two weights $w_{1}$ and $w_{2}$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration g. The tension in the string will be

A

$\frac{4w_{1}w_{2}}{w_{1}+w_{2}}$

B

$\frac{2w_{1}w_{2}}{w_{1}+w_{2}}$

C

$\frac{w_{1}-w_{2}}{w_{1}+w_{2}}$

D

$\frac{w_{1}w_{2}}{2(w_{1}+w_{2})}$

Question 107: Palette 107/135

Objective MCQ

A dynamometer D is attached to two bodies of masses M = 6 kg and m = 4 kg. Forces F = 20N and f = 10N are applied to the masses as shown. The dynamometer reads

A

$10\mathrm{N}$

B

$20\mathrm{N}$

C

$6\mathrm{N}$

D

$14\mathrm{N}$

Question 108: Palette 108/135

Objective MCQ

Two blocks are connected over a massless pulley as shown in figure. The mass of block A is 10 kg and the coefficient of kinetic friction is 0.2. Block A slides down the incline at constant speed. The mass of block B (in kg) is

A

5.4

B

3.3

C

4.2

D

6.8

Question 109: Palette 109/135

Objective MCQ

A block of mass 5 kg resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass 5 kg. The coefficient of kinetic friction between the block and the surface is 0.5. Tension in the cord is (Take, $g = 9.8 \, ms^{-2}$ )

A

$49\mathrm{N}$

B

zero

C

$36.75\mathrm{N}$

D

$12.75\mathrm{N}$

Question 110: Palette 110/135

Objective MCQ

A block of mass 3 kg is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be

A

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

B

$15\mathrm{N}$

C

$10\mathrm{N}$

D

$30\mathrm{N}$

Question 111: Palette 111/135

Objective MCQ

Two blocks of masses M and m are connected to each other by a massless string and spring of force constant k as shown in the figure. The spring passes over a frictionless pulley connected rigidly to the edge of a stationary block A. The coefficient of friction between block M and the plane horizontal surface of A is $\mu$ . The block M slides over the horizontal top surface of A and block m slides vertically downwards with the same speed. The mass M is equal to

A

$\frac{m}{\mu}$

B

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

C

$m\mu$

D

$\mu mg$

Question 112: Palette 112/135

Objective MCQ

A block of mass m, lying on a rough horizontal plane, is acted upon by a horizontal force P and another force Q, inclined at an angle $\theta$ to the vertical upwards. The block will remain in equilibrium, if minimum coefficient of friction between it and the surface is

A

$\frac{(P+Q\sin\theta)}{(mg-Q\cos\theta)}$

B

$\frac{(P\cos\theta+Q)}{(mg-Q\sin\theta)}$

C

$\frac{(P-Q\cos\theta)}{(mg+Q\sin\theta)}$

D

$\frac{(P\sin\theta-Q)}{(mg-Q\cos\theta)}$

Question 113: Palette 113/135

Objective MCQ

In the figure shown, if coefficient of friction is $\mu$ , then $m_{2}$ will start moving upwards, if

A

$\frac{m_1}{m_2} >\sin \theta -\mu \cos \theta$

B

$\frac{m_1}{m_2} >\sin \theta +\mu \cos \theta$

C

$\frac{m_1}{m_2} >\mu \sin \theta -\cos \theta$

D

$\frac{m_1}{m_2} >\mu \sin \theta +\cos \theta$

Question 114: Palette 114/135

Objective MCQ

A block of mass M rests on a rough horizontal surface as shown. Coefficient of friction between the block and the surface is $\mu$ . A force F = Mg acting at angle $\theta$ with the vertical side of the block pulls it. In which of the following cases, the block can be pulled along the surface?

A

$\tan\theta\geq\mu$

B

$\tan\left(\frac{\theta}{2}\geq\mu\right)$

C

$\cos \theta \geq \mu$

D

$\cot \left(\frac{\theta}{2}\right)\geq \mu$

Question 115: Palette 115/135

Objective MCQ

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

A

$F$

B

$\frac{F}{2}$

C

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

D

$3F$

Question 116: Palette 116/135

Objective MCQ

A uniform rope of length l lies on a table. If the coefficient of friction is $\mu$ , then the maximum length $l_{1}$ of the hanging part of the rope which can overhang from the edge of the table without sliding down is

A

$l/\mu$

B

$l/(\mu + 1)$

C

$\mu l / (\mu + 1)$

D

$\mu l / (\mu - 1)$

Question 117: Palette 117/135

Objective MCQ

Block A of mass m rests on the plank B of mass 3m which is free to slide on a frictionless horizontal surface. The coefficient of friction between the block and plank is 0.2. If a horizontal force of magnitude 2mg is applied to the plank B, the acceleration of A relative to the plank and relative to the ground respectively, are

A

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

B

$0, \frac{2g}{3}$

C

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

D

$\frac {2 g}{5}, \frac {g}{5}$

Question 118: Palette 118/135

Objective MCQ

Two blocks of masses m and 2m are placed one over the other as shown in figure. The coefficient of friction between m and 2m is $\mu$ and between 2m and ground is $\frac{\mu}{3}$ . If a horizontal force F is applied on upper block and T is tension developed in string, then choose the incorrect alternative.

A

If $F = \frac{\mu}{3} mg, T = 0$

B

If $F = \mu mg$ , $T = 0$

C

If $F = 2\mu mg, T = \frac{\mu mg}{3}$

D

If $F = 3\mu mg, T = 0$

Question 119: Palette 119/135

Objective MCQ

A block of mass m is placed on a wedge of mass 2 m which rests on a rough horizontal surface. There is no friction between the block and the wedge. The minimum coefficient of friction between the wedge and the ground, so that the wedge does not (a) 0.1 (b) 0.2 ground, so that the wedge does not move, is

A

0.1

B

0.2

C

0.3

D

0.4

Question 120: Palette 120/135

Objective MCQ

If the coefficient of friction between all surfaces is 0.4, then find the minimum force F to have equilibrium of the system. (Take, $g = 10 \, ms^{-2}$ )

A

$62.5\mathrm{N}$

B

$150\mathrm{N}$

C

$135\mathrm{N}$

D

$50\mathrm{N}$

Question 121: Palette 121/135

Objective MCQ

A sphere of mass m is held between two smooth inclined walls. For $\sin37^{\circ}=\frac{3}{5}$ , the normal reaction of the wall (2) is equal to

A

$\frac{16mg}{25}$

B

$\frac{25mg}{39}$

C

$\frac{39mg}{21}$

D

None of these

Question 122: Palette 122/135

Objective MCQ

A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string (i.e. angle $\theta$ ) when the trolley rolls up a plane of inclination $\alpha$ with acceleration a is

A

0

B

$\tan^{-1}\alpha$

C

$\tan^{-1}\left(\frac{a + g\sin\alpha}{g\cos\alpha}\right)$

D

$\tan^{-1}\frac{a}{g}$

Question 123: Palette 123/135

Objective MCQ

Assertion: When a person walks on a rough surface, the net force exerted by surface on the person is in the direction of his motion. Reason: It is the force exerted by the road on the person that causes the motion.

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 124: Palette 124/135

Objective MCQ

Assertion: A body of mass 10 kg is placed on a rough inclined surface ( $\mu = 0.7$ ). The surface is inclined to horizontal at angle 30°. Acceleration of the body down the plane will be zero. Reason: Force of friction is 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 125: Palette 125/135

Objective MCQ

Assertion: Static friction acting on a body is always greater than the kinetic friction acting on this body. Reason: Coefficient of static friction is more than the coefficient of kinetic friction.

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 126: Palette 126/135

Objective MCQ

Assertion: In the system of two blocks of equal masses as shown, the coefficient of friction between the blocks $(\mu_{2})$ is less than coefficient of friction $(\mu_{1})$ between lower block and ground. For all values of force F applied on upper block, lower block remains at rest. Reason: Frictional force on lower block due to upper block is not sufficient to overcome the frictional force on lower block due to ground.

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 127: Palette 127/135

Objective MCQ

Assertion: In the figure shown, block of mass m is stationary with respect to lift. Force of friction acting on the block is greater than $mg \sin \theta$ . Reason: If lift moves with constant velocity, then force of friction is equal to $mg \sin \theta$ .

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 128: Palette 128/135

Objective MCQ

Assertion: Block A is resting on one corner of a box as shown in figure. Acceleration of box is $(2\hat{\mathbf{i}} + 2\hat{\mathbf{j}})\mathrm{ms}^{-2}$ . Let $N_{1}$ is the normal reaction on block from vertical wall and $N_{2}$ from ground to box. Then, $\frac{N_{1}}{N_{2}} = \frac{1}{6}$ . (Neglect friction) Reason: $N_{1} = 0$ , if lift is stationary.

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 129: Palette 129/135

Objective MCQ

Which of the following statement (s) is/are correct?

A

The weighing machine measures the weight of a body.

B

During free fall of a person one feels weightlessness because his weight becomes zero.

C

During free fall, the person falls with an acceleration of g.

D

All of the above

Question 130: Palette 130/135

Objective MCQ

Which of the following statement (s) is/are incorrect?

A

Static friction is self-adjusting while kinetic friction is constant.

B

Friction always opposes the motion of two bodies.

C

Without friction, one can move on a smooth surface.

D

Some mechanical energy is lost in the form of heat due to air friction.

Question 131: Palette 131/135

Objective MCQ

Which of the following statement (s) is/are correct? I. A string has a mass m. If it is accelerated, tension is non-uniform and if it is not accelerated, tension is uniform. II. Tension force is an electromagnetic force.

A

Only I

B

Only II

C

Both I and II

D

None of these

Question 132: Palette 132/135

Objective MCQ

In the diagram shown in figure, string is massless and pulley is smooth, then which of the following statement (s) is/are correct? I. Net force on 1 kg block is $\frac{10}{3}$ N. II. Net force on both the blocks will be same.

A

Only I

B

Only II

C

Both I and II

D

None of these

Question 133: Palette 133/135

Objective MCQ

Two forces are acting on a rope lying on a smooth table as shown in figure. Which of the following statement (s) is/are correct? I. In moving from A to B, tension on string decreases from 2F to F. II. Situation will becomes indeterminant, if we take it a massless string.

A

Only I

B

Only II

C

Both I and II

D

None of these

Question 134: Palette 134/135

Objective MCQ

In the figure, block A and B of masses 2m and m are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses 2m and m just after the instant when the string of mass m is cut

A

g, g

B

g, g/2

C

g/2, g

D

g/2, g/2

Question 135: Palette 135/135

Objective MCQ

Three identical blocks of masses m = 2 kg are drawn by a force 10.2 N on a frictionless surface. What is the tension (in newton) in the string between the blocks B and C?

A

9.2

B

8

C

3.4

D

9.8