Question 1: Palette 1/293

Errorless NEET 2024 MCQ

A horizontal force 10 N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg respectively. The blocks slide over a frictionless surface. The force exerted by block A on block B is

A

Zero

B

$4N$

C

$6N$

D

$10N$

Question 2: Palette 2/293

Errorless JEE (Main) 2023 MCQ

Given below are two statements: Statement-I: ASn elevator can go up or dwon with uniform speed when its weight is balanced with the tensionn of its cable Statement-II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 3: Palette 3/293

Errorless JEE (Main) 2023 MCQ

Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be

A

40 N

B

5 N

C

20 N

D

10 N

Question 4: Palette 4/293

Errorless JEE (Main) 2023 MCQ

A block of $\sqrt{3}$ kg is attached to a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension T is (Given $g = 10 ms^{-2}$ )

A

20 N

B

25 N

C

10 N

D

15 N

Question 5: Palette 5/293

Errorless JEE (Main) 2023 MCQ

A machine gun of mass 10kg fires 20g bullets at the rate of 180 bullets per minute with a speed of $100ms^{-1}$ each. The recoil velocity of the gun is

A

0.02m/s

B

2.5m/s

C

1.5m/s

D

0.6m/s

Question 6: Palette 6/293

Errorless JEE (Main) 2023 MCQ

100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time t s. The total force exerted by the balls on the wall is

A

$\frac{100\,mv}{t}$

B

$\frac{200\,mv}{t}$

C

200 mvt

D

$\frac{mv}{100\,t}$

Question 7: Palette 7/293

Errorless NEET 2023 MCQ

A football player is moving southward and suddenly turns eastward with the same speed to avoid opponent. The force that acts on the player while turning is

A

Along northward

B

Along north - east

C

Along south - west

D

Along eastward

Question 8: Palette 8/293

Errorless NEET 2023 MCQ

A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$ . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is

A

24 cm

B

28 cm

C

30 cm

D

27 cm

Question 9: Palette 9/293

Errorless JEE (Main) 2023 MCQ

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

A

0.33

B

0.5m

C

3.2m

D

0.8m

Question 10: Palette 10/293

Errorless JEE (Main) 2023 MCQ

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34 [Take $g = 10 ms^{-2}$ ]

A

$3.4 ms^{-1}$

B

$22.4 ms^{-1}$

C

$13 ms^{-1}$

D

$17 ms^{-1}$

Question 11: Palette 11/293

Errorless JEE (Main) 2023 MCQ

A body of mass 10kg is moving with an initial speed of 20m/s. The body stops after 5s due to friction between body and the floor. The value of the coefficient of friction is (Take acceleration due to gravity $g = 10ms^{-2}$ )

A

0.2

B

0.3

C

0.5

D

0.4

Question 12: Palette 12/293

Errorless JEE (Main) 2023 MCQ

A block of mass 5kg is placed at rest on a table of rough surface. Now, if a force of 30N is applied in the direction parallel to surface of the table, the block slides through a distance of 50m in an interval of time 10s. Coefficient of kinetic friction is (given, $g = 10ms^{-2}$ )

A

0.60

B

0.75

C

0.50

D

0.25

Question 13: Palette 13/293

Errorless JEE (Main) 2022 MCQ

A block of mass M placed inside a box descends vertically with acceleration ‘a’. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ‘a’ will be

A

$\frac{g}{4}$

B

$\frac{g}{2}$

C

$\frac{3g}{4}$

D

g

Question 14: Palette 14/293

Errorless JEE (Main) 2022 MCQ

A body of mass M at rest explodes into three pieces, in the ratio of masses 1:1:2. Two smaller pieces fly off perpendicular to each other with velocities of $30 \, ms^{-1}$ and $40 \, ms^{-1}$ respectively. The velocity of the third piece will be

A

$15 \, ms^{-1}$

B

$25 \, ms^{-1}$

C

$35 \, ms^{-1}$

D

$50 \, ms^{-1}$

Question 15: Palette 15/293

Errorless JEE (Main) 2022 MCQ

A person is standing in an elevator. In which situation, he experiences weight loss

A

When the elevator moves upward with constant acceleration

B

When the elevator moves downward with constant acceleration

C

When the elevator moves upward with uniform velocity

D

When the elevator moves downward with uniform velocity

Question 16: Palette 16/293

Errorless JEE (Main) 2022 MCQ

Two billiard balls of mass 0.05 kg each moving in opposite directions with $10 \, ms^{-1}$ collide and rebound with the same speed. If the time duration of contact is t = 0.005s, then what is the force exerted on the ball due to each other

A

100 N

B

200 N

C

300 N

D

400 N

Question 17: Palette 17/293

Errorless JEE (Main) 2022 MCQ

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero

A

$\sqrt{2} N, 45^{\circ}$

B

$\sqrt{2} N, 135^{\circ}$

C

$\frac{2}{\sqrt{3}} N, 30^{\circ}$

D

$2N, 45^{\circ}$

Question 18: Palette 18/293

Errorless JEE (Main) 2022 MCQ

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne)

A

3

B

9

C

12

D

18

Question 19: Palette 19/293

Errorless NEET 2022 MCQ

A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2:2:1. If the fragments having equal mass fly off along mutually perpendicular directions with speed v, the speed of the third (lighter) fragment is

A

$2\sqrt{2}v$

B

$3\sqrt{2}v$

C

v

D

$\sqrt{2}v$

Question 20: Palette 20/293

Errorless JEE (Main) 2022 MCQ

A block of mass 10kg starts sliding on a surface with an initial velocity of $9.8 \, ms^{-1}$ . The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is [use $g = 9.8 \, ms^{-2}$ ]

A

4.9 m

B

9.8 m

C

12.5 m

D

19.6 m

Question 21: Palette 21/293

Errorless JEE (Main) 2022 MCQ

A bag is gently dropped on a conveyor belt moving at a speed of 2m/s. The coefficient of friction between the conveyor belt and bag is 0.4. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is [Take $g = 10 \, m/s^{2}$ ]

A

2 m

B

0.5 m

C

3.2 m

D

0.8 m

Question 22: Palette 22/293

Errorless JEE (Main) 2021 MCQ

Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be

A

$\sqrt{3}T$

B

$\frac{T}{\sqrt{3}}$

C

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

D

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

Question 23: Palette 23/293

Errorless JEE (Main) 2021 MCQ

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

A

$2F_{0}T/M$

B

$F_{0}T/2M$

C

$4F_{0}T/3M$

D

$F_{0}T/3M$

Question 24: Palette 24/293

Errorless JEE (Main) 2021 MCQ

A force $\vec{F} = (40\hat{i} + 10\hat{j})N$ acts on a body of mass $5\mathrm{kg}$ . If the body starts from rest, its position vector $\vec{r}$ at time $t = 10s$ , will be

A

$(100\hat{i} + 400\hat{j})m$

B

$(100\hat{i} + 100\hat{j})m$

C

$(400\hat{i} + 100\hat{j})m$

D

$(400\hat{i} + 400\hat{j})m$

Question 25: Palette 25/293

Errorless JEE (Main) 2021 MCQ

A steel block of 10kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2m/s^{2}$ . The normal reaction $R'$ by the floor if mass of the iron cylinders are equal and of 20kg each, is ____ N [Take $g = 10m/s^{2}$ and $\mu_{s} = 0.2$ ] $a = 0.2m / s^{2}$

A

716

B

686

C

714

D

684

Question 26: Palette 26/293

Errorless JEE (Main) 2021 MCQ

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be

A

$100\%$

B

$200\%$

C

$300\%$

D

$400\%$

Question 27: Palette 27/293

Errorless JEE (Main) 2021 MCQ

A bullet of '4g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of $50ms^{-1}$ , the impulse imparted to the gun and velocity of recoil of gun are

A

$0.4kg ms^{-1}, 0.1ms^{-1}$

B

$0.2kg ms^{-1}, 0.05ms^{-1}$

C

$0.2kg ms^{-1}, 0.1ms^{-1}$

D

$0.4kg ms^{-1}, 0.05ms^{-1}$

Question 28: Palette 28/293

Errorless JEE (Main) 2021 MCQ

Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is ball (a) ball (b)

A

1:1

B

$\sqrt{2}:1$

C

$2:1$

D

$1:\sqrt{2}$

Question 29: Palette 29/293

Errorless 2021 MCQ

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that rocket is given an acceleration of $20 \, ms^{-2}$ . The gases come out at a relative speed of $500 \, ms^{-1}$ with respect to the rocket [Use $g = 10 \, m/s^{2}$ ] (JEE (Main) 2021)

A

$6.0 \times 10^{2} \, kg s^{-1}$

B

$500 \, kg s^{-1}$

C

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

D

$60 \, kg s^{-1}$

Question 30: Palette 30/293

Errorless JEE (Main) 2021 MCQ

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to

A

$\sqrt{\frac{m_{p}}{m_{e}}}$

B

$\sqrt{\frac{m_{e}}{m_{p}}}$

C

$\frac{m_{p}}{m_{e}}$

D

$\left(\frac{m_{p}}{m_{e}}\right)^{3/2}$

Question 31: Palette 31/293

Errorless JEE (Main) 2021 MCQ

Two blocks of masses 3 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2} N m^{-2}$ . What is the minimum radius of the wire (take $g = 10 m s^{-2}$ )

A

1250 cm

B

1.25 cm

C

125 cm

D

12.5 cm

Question 32: Palette 32/293

Errorless JEE (Main) 2021 MCQ

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

A

$0.25\mathrm{s}$

B

$0.34s$

C

$0.2s$

D

$0.4s$

Question 33: Palette 33/293

Errorless JEE (Main) 2021 MCQ

Angular momentum of a single particle moving with constant speed along circular path

A

Changes in magnitude but remains same in the direction

B

Is zero

C

Remains same in magnitude and direction

D

Remains same in magnitude but changes in the direction

Question 34: Palette 34/293

Errorless NEET 2021 MCQ

A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is $(g = 10m/s^{2})$ nearly

A

4.2 kg m/s

B

2.1 kg m/s

C

1.4 kg m/s

D

0 kg m/s

Question 35: Palette 35/293

Errorless NEET 2021 MCQ

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass ‘m’ is suspended from the rod at 160 cm mark as shown in the figure. Find the value of ‘m’ such that the rod is in equilibrium ( $g = 10 \, m/s^{2}$ )

A

$\frac {1}{3} k g$

B

$\frac {1}{6} k g$

C

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

D

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

Question 36: Palette 36/293

Errorless JEE (Main) 2021 MCQ

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

A

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

B

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

C

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

D

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

Question 37: Palette 37/293

Errorless JEE (Main) 2021 MCQ

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is [The coefficient of static friction, $\mu_{s}$ is 0.4]

A

$\frac{7}{2} mg$

B

$5mg$

C

$\frac{mg}{5}$

D

0

Question 38: Palette 38/293

Errorless JEE (Main) 2021 MCQ

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is ____ $\times 10^{3}$ kg m/s $^{2}$

A

10.2

B

7.2

C

12.4

D

6.96

Question 39: Palette 39/293

Errorless NEET 2021 MCQ

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

A

8.1 kW

B

12.3 kW

C

7.0 kW

D

10.2 kW

Question 40: Palette 40/293

Errorless JEE (Main) 2020 MCQ

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

A

100 N

B

90 N

C

75 N

D

70 N

Question 41: Palette 41/293

Errorless JEE (Main) 2020 MCQ

A uniformly thick wheel with moment of inertia $I$ and radius $R$ is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses $m_1$ and $m_2(m_1 > m_2)$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $m_1$ descents by a distance $h$ is

A

$\left[\frac{m_1 + m_2}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}gh$

B

$\left[\frac{2(m_1 - m_2)gh}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}$

C

$\left[\frac{2(m_1 + m_2)gh}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}$

D

$\left[\frac{(m_1 - m_2)}{(m_1 + m_2)R^2 + I}\right]^{\frac{1}{2}}gh$

Question 42: Palette 42/293

Errorless NEET 2020 MCQ

Two bodies of mass 4kg and 6kg 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

$g / 10$

B

$g$

C

$g / 2$

D

$g / 5$

Question 43: Palette 43/293

Errorless JEE (Main) 2020 MCQ

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

A

0.80 m

B

0.60 m

C

0.45 m

D

0.20 m

Question 44: Palette 44/293

Errorless JEE (Main) 2019 MCQ

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of $45^{\circ}$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is $(g = 10 \, ms^{-2})$

A

200 N

B

100 N

C

140 N

D

70 N

Question 45: Palette 45/293

Errorless JEE (Main) 2019 MCQ

A block of mass $10\mathrm{kg}$ is kept on a rough inclined plane as shown in the figure. A force of $3N$ is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force $P$ , such that the block does not move downward (Take $g = 10ms^{-2}$ )

A

$32N$

B

$25N$

C

$23N$

D

$18N$

Question 46: Palette 46/293

Errorless JEE (Main) 2019 MCQ

A particle of mass m is moving in a straight line with momentum p. Starting at time t=0, a force F=kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is

A

$2\sqrt{\frac{p}{k}}$

B

$\sqrt{\frac{2p}{k}}$

C

$\sqrt{\frac{2k}{p}}$

D

$2\sqrt{\frac{k}{p}}$

Question 47: Palette 47/293

Errorless JEE (Main) 2019 MCQ

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height $(p-h)$ diagram is

A

B

C

D

Question 48: Palette 48/293

Errorless JEE (Main) 2019 MCQ

A bullet of mass 20 g has an initial speed of $1ms^{-1}$ , just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of $2.5 \times 10^{-2}N$ , the speed of the bullet after emerging from the other side of the wall is close to

A

$0.4 ms^{-1}$

B

$0.1 ms^{-1}$

C

$0.3 ms^{-1}$

D

$0.7 ms^{-1}$

Question 49: Palette 49/293

Errorless JEE (Main) 2019 MCQ

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70 \, ms^{-1}$ with respect to the man. The speed of the man with respect to the surface is

A

$0.20 \, ms^{-1}$

B

$0.14 \, ms^{-1}$

C

$0.47 \, ms^{-1}$

D

$0.28 \, ms^{-1}$

Question 50: Palette 50/293

Errorless JEE (Main) 2019 MCQ

A block kept on a rough inclined plane, as shown in the figure, remains at rest up to a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. the coefficient of static friction between the block and the plane is [Take $g = 10m / s^2$ ]

A

$\frac{2}{3}$

B

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

C

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

D

$\frac{1}{2}$

Question 51: Palette 51/293

Errorless JEE (Main) 2019 MCQ

Two blocks A and B of masses $m_{A}=1kg$ and $m_{B}=3kg$ are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally. So that the block A does not slide over the block B is [Take $g = 10m / s^2$ ]

A

16 N

B

40 N

C

12 N

D

8 N

Question 52: Palette 52/293

Errorless JEE (Main) 2019 MCQ

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F=20 N, making an angle of $30^{\circ}$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu=0.2$ . The difference between the accelerations of the block, in case (B) and case (A) will be $(g=10\ ms^{-2})$

(A)

(B)

A

$0ms^{-2}$

B

$0.8ms^{-2}$

C

$0.4ms^{-2}$

D

$3.2ms^{-2}$

Question 53: Palette 53/293

Errorless JEE (Main) 2018 MCQ

The mass of a hydrogen molecule is $3.32 \times 10^{-27}$ kg. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2 cm^{2}$ at an angle of $45^{\circ}$ to the normal, and rebound elastically with a speed of $10^{3}$ m/s, then the pressure on the wall is nearly

A

$4.70 \times 10^{3}$ $N/m^{2}$

B

$2.35 \times 10^{2}$ $N/m^{2}$

C

$4.70 \times 10^{2}$ $N/m^{2}$

D

$2.35 \times 10^{3}$ $N/m^{2}$

Question 54: Palette 54/293

Errorless NEET 2018 MCQ

Which one of the following statements is incorrect

A

Rolling friction is smaller than sliding friction

B

Limiting value of static friction is directly proportional to normal reactions

C

Frictional force opposes the relative motion

D

Coefficient of sliding friction has dimensions of length

Question 55: Palette 55/293

Errorless NEET (Phase-II) 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 below. The value of impulse imparted by the wall in the ball will be

A

$\frac{mV}{3}$

B

mV

C

2mV

D

$\frac{mV}{2}$

Question 56: Palette 56/293

Errorless WB-JEE 2016 MCQ

An explosive of mass 9 kg is divided in two parts. One part of mass 3 kg moves with velocity of 16 m/s. The kinetic energy of other part will be

A

192 J

B

162 J

C

150 J

D

200 J

Question 57: Palette 57/293

Errorless WB-JEE 2016 MCQ

A mass m rests on another mass M. The co-efficient of static friction between B the surfaces of m and M is $\mu$ . M rests on a smooth frictionless horizontal plane. The maximum force applied horizontally on M for which m will move along with M without slipping is

A

$mg + \mu mg$

B

$(M + m)\mu g$

C

$\frac{mM}{M + m}\mu g$

D

$\mu mg$

Question 58: Palette 58/293

Errorless NEET (Phase-I) 2016 MCQ

A car is negotiating a curved road of radius R. The road is banked at an angle $\theta$ . The coefficient of friction between the tyres of the car and the road is $\mu_{s}$ . The maximum safe velocity on this road is

A

$\sqrt{gR^{2}\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$

B

$\sqrt{gR\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$

C

$\sqrt{\frac{g}{R}\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$

D

$\sqrt{\frac{g}{R^{2}}\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$

Question 59: Palette 59/293

Errorless 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 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 60: Palette 60/293

Errorless JEE (Main) 2015 MCQ

Given in the figure are two blocks $A$ and $B$ of weight $20N$ and $100N$ , respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is 0.1 and between block $B$ and the wall is 0.15, the frictional force applied by the wall on block $B$ is

A

100 N

B

80 N

C

120 N

D

150 N

Question 61: Palette 61/293

Errorless AIPMT (Cancelled) 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

$\frac{(m_2 - \mu km_1)g}{(m_1 + m_2)}$

B

$\frac{m_1m_2(1 + \mu_k)g}{(m_1 + m_2)}$

C

$\frac{m_1m_2(1 - \mu_k)g}{(m_1 + m_2)}$

D

$\frac{(m_2 + \mu_km_1)g}{(m_1 + m_2)}$

Question 62: Palette 62/293

Errorless AIPMT 2015 MCQ

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^{\circ}$ the box starts to slip and slides 4.0 m down the plank in 4.0s. The coefficients of static and kinetic friction between the box and the plank will be, respectively

A

0.6 and 0.5

B

0.5 and 0.6

C

0.4 and 0.3

D

0.6 and 0.6

Question 63: Palette 63/293

Errorless GUJCET 2015 MCQ

An inclined plane of length 5.60 m making an angle of $45^{\circ}$ with the horizontal is placed in an uniform electric field $E = 100 V m^{-1}$ . A particle of mass 1 kg and charge $10^{-2} C$ is allowed to slide down from rest position from maximum height of slope. If the co-efficient of friction is 0.1, the time taken by the particle to reach the bottom is

A

1 s

B

1.41 s

C

2 s

D

None of these

Question 64: Palette 64/293

Errorless CBSE PMT 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

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

B

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

C

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

D

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

Question 65: Palette 65/293

Errorless CBSE PMT 2014 MCQ

A body of mass 3kg is acted on by a force which varies as shown in the graph below. The momentum acquired is given by

A

Zero

B

$5N - s$

C

30 N-s

D

50 N-s

Question 66: Palette 66/293

Errorless JEE (Main) 2014 MCQ

A block of mass m is placed on a surface with a vertical cross section given by $y=\frac{x^{3}}{6}$ . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is

A

1/6 m

B

2/3 m

C

1/3 m

D

1/2 m

Question 67: Palette 67/293

Errorless WB-JEE 2013 MCQ

A shell of mass $5M$ , acted upon by no external force and initially at rest, bursts into three fragments of masses $M$ , $2M$ and $2M$ respectively. The first two fragments move in opposite directions with velocities of magnitudes $2V$ and $V$ respectively. The third fragment will

A

Move with a velocity $V$ in a direction perpendicular to the other two

B

Move with a velocity $2V$ in the direction of velocity of the first fragment

C

Be at rest

D

Move with a velocity $V$ in the direction of velocity of the second fragment

Question 68: Palette 68/293

Errorless NEET 2013 MCQ

Three blocks with masses m, 2m and 3m are connected by strings, as shown in 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

6 mg

B

Zero

C

2 mg

D

3 mg

Question 69: Palette 69/293

Errorless MP PET 2013 MCQ

A cylinder rolls up an inclined plane, reaches some height and then rolls down without slipping throughout these motions. The directions of the frictional force acting on the cylinder are

A

Up the incline while ascending and down the incline while descending

B

Up the incline while descending and down the incline while ascending

C

Down the incline while ascending and descending

D

Up the incline while ascending and descending

Question 70: Palette 70/293

Errorless AMU (Engg.) 2012 MCQ

A body of mass 0.4 kg starting at origin at t = 0 with a speed of 10 m/s in the positive x-axis direction is subjected to a constant force F = 8 N towards negative x-axis. Calculate the position of the particle after 25 seconds

A

-6000 m

B

-8000 m

C

+4000 m

D

+7000 m

Question 71: Palette 71/293

Errorless Kerala PMT 2012 MCQ

A batsman hits back a ball of mass 0.15kg straight in the direction of the bowler without changing its initial speed of $10ms^{-1}$ . If the ball moves linearly, then the impulse imparted on it (in Ns) is

A

3.0

B

2.0

C

1.5

D

1.9

E

0

Question 72: Palette 72/293

Errorless Kerala PET 2012 MCQ

The sum of magnitudes of two forces acting at a point is 16 N and their resultant $8\sqrt{3}$ N is at $90^{\circ}$ with the force of smaller magnitude. The two forces (in N) are

A

11, 5

B

9, 7

C

6, 10

D

4, 12

E

2, 14

Question 73: Palette 73/293

Errorless WB-JEE 2012; AIPMT (Cancelled) 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

6N

B

8N

C

18N

D

2N

Question 74: Palette 74/293

Errorless J & K CET 2012 MCQ

Two blocks, of mass 1 kg and 2 kg respectively, are connected by a spring and kept on a frictionless table. The blocks are pulled apart, so that the spring is stretched, and released from rest. At a certain instant of time, the block of mass 1 kg, is found to be moving at a speed 2 m/s. What must be the speed of the other block at this instant

A

1 m/s

B

0.5 m/s

C

4 m/s

D

0.25 m/s

Question 75: Palette 75/293

Errorless Kerala PET 2012 MCQ

A block of mass 10 kg is moving horizontally with a speed of $1.5 \, ms^{-1}$ on a smooth plane. If a constant vertical force 10 N acts on it, the displacement of the block from the point of application of the force at the end of 4 seconds is

A

5 m

B

20 m

C

12 m

D

10 m

E

18 m

Question 76: Palette 76/293

Errorless Kerala PET 2012 MCQ

A block of weight 4 kg is resting on a smooth horizontal plane. If it is struck by a jet of water at the rate of $2kgs^{-1}$ and at the speed of $10ms^{-1}$ , then the initial acceleration of the block is

A

$15ms^{-2}$

B

$10ms^{-2}$

C

$2.5ms^{-2}$

D

$1ms^{-2}$

E

$5ms^{-2}$

Question 77: Palette 77/293

Errorless AMU (Engg.) 2012 MCQ

A block of mass 15 kg is held by a string on an inclined plane (angle $30^{\circ}$ ). The tension T in the string is $(g=10\ m/s^{2})$

A

55 N

B

60 N

C

75 N

D

90 N

Question 78: Palette 78/293

Errorless AIEEE 2012 MCQ

A particle of mass $m$ is at rest at the origin at time $t = 0$ . It is subjected to a force $F(t) = F_0 e^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves

A

B

C

D

Question 79: Palette 79/293

Errorless WB JEE 2012 MCQ

A box of mass 2kg is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. Coefficient of static friction between the box and the roof of the car is 0.2 and $g = 10 \, ms^{-2}$ This maximum acceleration of the car, for the box to remain stationary, is

A

$8 \, ms^{-2}$

B

$6 \, ms^{-2}$

C

$4 \, ms^{-2}$

D

$2 \, ms^{-2}$

Question 80: Palette 80/293

Errorless CBSE PMT (Mains) 2012 MCQ

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu$ , is

A

$\mu Rg$

B

$Rg\sqrt{\mu}$

C

$\mu \sqrt{Rg}$

D

$\sqrt{\mu Rg}$

Question 81: Palette 81/293

Errorless AMU (Med.) 2012 MCQ

In the figure given, the system is in equilibrium. What is the maximum value that W can have if the friction force on the 40 N block cannot exceed 12.0 N

A

3.45 N

B

6.92 N

C

10.35 N

D

12.32 N

Question 82: Palette 82/293

Errorless Kerala PMT 2012 MCQ

Identify the correct statement

A

Static friction depends on the area of contact

B

Kinetic friction depends on the area of contact

C

Coefficient of kinetic friction does not depend on the surfaces in contact

D

Coefficient of static friction does not depend on the surfaces in contact

E

Coefficient of kinetic friction is less than the coefficient of static friction

Question 83: Palette 83/293

Errorless Kerala PET 2011 MCQ

Two masses $m_{1}=1kg$ and $m_{2}=2kg$ are connected by a light inextensible string and suspended by means of a weightless pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in two seconds is (Take $g=10ms^{-2}$ )

A

$\frac{20}{9}m$

B

$\frac{40}{9}m$

C

$\frac{2}{3}m$

D

$\frac{1}{3}m$

E

4m

Question 84: Palette 84/293

Errorless Odisha JEE 2011 MCQ

The acceleration of system of two bodies over the wedge as shown in figure is

A

$1ms^{-2}$

B

$2ms^{-2}$

C

$0.5ms^{-2}$

D

$10ms^{-2}$

Question 85: Palette 85/293

Errorless Odisha JEE 2011 MCQ

In relativity which is constant between two frames of reference

A

Acceleration

B

Conservation of mass

C

Space interval

D

Velocity

Question 86: Palette 86/293

Errorless Odisha JEE 2011 MCQ

A man drags a block through 10m on rough surface ( $\mu=0.5$ ). A force of $\sqrt{3}kN$ acting at $30^{\circ}$ to the horizontal. The work done by applied force is

A

Zero

B

15 kJ

C

5 kJ

D

10 kJ

Question 87: Palette 87/293

Errorless Kerala PET 2011 MCQ

A block at rest slides down a smooth inclined plane which makes an angle $60^{\circ}$ with the vertical and it reaches the ground in $t_1$ seconds. Another block is dropped vertically from the same point and reaches the ground in $t_2$ seconds. Then the ratio of $t_1:t_2$ is

A

$1:2$

B

$2:1$

C

$1:3$

D

$1:\sqrt{2}$

E

$3:1$

Question 88: Palette 88/293

Errorless Kerala PET 2010 MCQ

A man getting down a running bus falls forward because

A

Due to inertia of rest, road is left behind and man reaches forward

B

Due to inertia of motion upper part of body continues to be in motion in forward direction while feet come to rest as soon as they touch the road

C

He leans forward as a matter of habit

D

Of the combined effect of all the three factors stated in (a),

Question 89: Palette 89/293

Errorless Kerala PMT 2010 MCQ

Human heart is pumping blood with constant velocity $v \, m \, s^{-1}$ at the rate of $M \, kg \, s^{-1}$ . The force required for this is (in N)

A

M

B

$Mv$

C

$\frac{M}{v}$

D

$v \frac{dM}{dt}$

E

$M \frac {d v}{d t}$

Question 90: Palette 90/293

Errorless DUMET 2010 MCQ

A person is measuring his weight by standing on a weighing machine inside a lift. When the lift is at rest, the machine shows his weight to be 55 kg. In between the floor when the lift is moving up with a constant speed of 10 km/hr, he again measures his weight, which is

A

55 kg

B

65 kg

C

50 kg

D

45 kg

Question 91: Palette 91/293

Errorless J & K CET 2010 MCQ

Rocket propulsion is associated with

A

The conservation of angular momentum

B

The conservation of mass

C

The conservation of mechanical energy

D

Newton's III law of motion

Question 92: Palette 92/293

Errorless DUMET 2010 MCQ

In an air collision between an aeroplane and a bird, the force experienced by the bird as compared to that of the aeroplane is

A

Very high

B

Equal

C

Less

D

Zero

Question 93: Palette 93/293

Errorless J & K CET 2010 MCQ

Three forces $F_{1}, F_{2}$ and $F_{3}$ together keep a body in equilibrium. If $F_{1} = 3N$ along the positive $x$ -axis, $F_{2} = 4N$ along the positive $y$ -axis, then the third force $F_{3}$ is

A

5 N making an angle $\theta = \tan^{-1}\left(\frac{3}{4}\right)$ with negative y-axis

B

5 N making an angle $\theta = \tan^{-1}\left(\frac{4}{3}\right)$ with negative y axis

C

7 N making an angle $\theta = \tan^{-1}\left(\frac{3}{4}\right)$ with negative y axis

D

7 N making an angle $\theta = \tan^{-1}\left(\frac{4}{3}\right)$ with negative y axis

Question 94: Palette 94/293

Errorless MP PET 2010 MCQ

A block of Mass M placed on a frictionless horizontal table is pulled by another block of mass m hanging vertically by a massless string passing over a frictionless pully. The tension in the string is

A

$\frac{m}{M+m}g$

B

$\frac{M}{M+m}g$

C

$\frac{M+m}{Mm}g$

D

$\frac{Mm}{M+m}g$

Question 95: Palette 95/293

Errorless AIEEE 2010 MCQ

Two fixed frictionless inclined planes making an angle $30^{\circ}$ and $60^{\circ}$ with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B

A

$4.9ms^{-2}$ in vertical direction

B

$4.9ms^{-2}$ in horizontal direction

C

$9.8ms^{-2}$ in vertical direction

D

Zero

Question 96: Palette 96/293

Errorless AIEEE 2010 MCQ

The figure shows the position - time $(x - t)$ graph of one-dimensional motion of a body of mass $0.4\mathrm{kg}$ . The magnitude of each impulse is

A

$0.2\mathrm{Ns}$

B

0.4 Ns

C

0.8 Ns

D

1.6 Ns

Question 97: Palette 97/293

Errorless Kerala PET 2010 MCQ

Which one of the following is not a contact force

A

Viscous force

B

Air resistance

C

Friction

D

Buoyant force

E

Magnetic force

Question 98: Palette 98/293

Errorless DUMET 2010 MCQ

An iron block of mass 5 kg is kept on a trolley. If the trolley is being pushed with an acceleration of $5 \, m/s^{2}$ , What will be the force of friction between the block and the trolley surface (Take the coefficient of static friction between the block and the surface to be 0.8)

A

Zero

B

5 N

C

4 N

D

25 N

Question 99: Palette 99/293

Errorless CBSE PMT 2010 MCQ

A gramophone record is revolving with an angular velocity $\omega$ . A coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$ . The coin will revolve with the record if

A

$r \geq \frac{\mu g}{\omega^2}$

B

$r = \mu g \omega^2$

C

$r < \frac{\omega^2}{\mu g}$

D

$r \leq \frac{\mu g}{\omega^2}$

Question 100: Palette 100/293

Errorless J & K CET 2010 MCQ

An object placed on an inclined plane starts sliding when the angle of incline becomes $30^{\circ}$ . The coefficient of static friction between the object and the plane is

A

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

B

$\sqrt{3}$

C

$\frac{1}{2}$

D

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

Question 101: Palette 101/293

Errorless CBSE PMT 2010 MCQ

A block of mass $m$ is in contact with the cart $C$ as shown in the figure The coefficient of static friction between the block and the cart is $\mu$ . The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies

A

$\alpha < \frac{g}{\mu}$

B

$\alpha > \frac{mg}{\mu}$

C

$\alpha > \frac{g}{\mu m}$

D

$\alpha \geq \frac{g}{\mu}$

Question 102: Palette 102/293

Errorless Odisha JEE 2010 MCQ

A boy presses a book against the front wall such that the book does not move. The force of friction between the wall and the book is

A

Towards right

B

Towards left

C

Downwards

D

Upwards

Question 103: Palette 103/293

Errorless Odisha JEE 2009 MCQ

The velocity of a body of mass 20 kg decreases from 20 m/s to 5 m/s in a distance of 100 m. Force on the body is

A

-27.5 N

B

-47.5 N

C

-37.5 N

D

-67.5 N

Question 104: Palette 104/293

Errorless MP PMT 2009, 10 MCQ

Formula for true force is

A

$F = ma$

B

$F = \frac{md\nu}{dt}$

C

$F = \frac{dm\nu}{dt}$

D

$F = \frac{md^2x}{dt^2}$

Question 105: Palette 105/293

Errorless KCET 2009 MCQ

A body of mass 0.05 kg is observed to fall with an acceleration of $9.5 \, ms^{-2}$ . The opposing force of air on the body is $(g = 9.8 \, ms^{-2})$

A

0.015 N

B

0.15 N

C

0.030 N

D

Zero

Question 106: Palette 106/293

Errorless AMU PMT 2009 MCQ

A 10 kg stone is suspended with a rope of breaking strength 30 kg wt. The minimum time in which the stone can be raised through a height 10 m starting from rest is (taking g = 10 N/kg)

A

0.5 seconds

B

1.0 seconds

C

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

D

2.0 seconds

Question 107: Palette 107/293

Errorless Kerala PET 2009 MCQ

A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass $(m/3)$ is fixed to the block, which is pulled in the horizontal direction by applying a force F at the other end. The tension in the middle of the rope is

A

$\frac{8}{7}F$

B

$\frac{1}{7}F$

C

$\frac{1}{8}F$

D

$\frac{1}{5}F$

E

$\frac{7}{8}F$

Question 108: Palette 108/293

Errorless AMU (Engg.) 2009 MCQ

A particle moves in the $x - y$ plane under the influence of a force such that its linear momentum is $\vec{p}(t) = A[\hat{i}\cos (kt) - \hat{j}\sin (kt)]$ where $A$ and $k$ are constants. The angle between the force and momentum is

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$90^{\circ}$

Question 109: Palette 109/293

Errorless AMU PMT 2009 MCQ

Ten one-rupee coins are put on top of each other on a table. Each coin has a mass $m$ . which of the following statements is not true

A

The force on the $6^{th}$ coins (counted from the bottom) due to all the coins on its top is equal to 4 mg (downwards)

B

The force on $6^{th}$ coin due to $7^{th}$ coin is 4mg (downwards)

C

The reaction of the $6^{th}$ coin on the $7^{th}$ coin is 4mg (upwards)

D

The total force on the $10^{\text{th}}$ coin is 9 mg (downwards)

Question 110: Palette 110/293

Errorless CBSE PMT 2009; NEET 2013 MCQ

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of $12 \, ms^{-1}$ and 2 kg second part moving with a velocity of $8 \, ms^{-1}$ . If the third part flies off with a velocity of $4 \, ms^{-1}$ , its mass would be

A

5 kg

B

7 kg

C

17 kg

D

3 kg

Question 111: Palette 111/293

Errorless Kerala PET 2009 MCQ

A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with a velocity of $3\hat{i}ms^{-1}$ and the other with a velocity of $4\hat{j}ms^{-1}$ . If the explosion occurs in $10^{-4}s$ , the average force acting on the third piece in newton is

A

$(3\hat{i} + 4\hat{j})\times 10^{-4}$

B

$(3\hat{i} - 4\hat{j})\times 10^{-4}$

C

$(3\hat{i} + 4\hat{j})\times 10^{4}$

D

$-(3\hat{i} + 4\hat{j})\times 10^{4}$

E

$(4\hat{i} - 3\hat{j})\times 10^{4}$

Question 112: Palette 112/293

Errorless Kerala PMT 2009 MCQ

Newton's second and third laws of motion lead to the conservation of

A

Linear momentum

B

Angular Momentum

C

Potential energy

D

Kinetic energy

E

Force

Question 113: Palette 113/293

Errorless Odisha JEE 2009 MCQ

A bullet of mass 10 g moving with 300 m/s hits a block of ice of mass 5 kg and drops dead. The velocity of ice is

A

50 cm/s

B

60 cm/s

C

40 cm/s

D

30 cm/s

Question 114: Palette 114/293

Errorless IIT-JEE 2009 MCQ

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

A

Linear momentum of the system does not change in time

B

Kinetic energy of the system does not change in time

C

Angular momentum of the system does not change in time

D

Potential energy of the system does not change in time

Question 115: Palette 115/293

Errorless KCET 2009 MCQ

Three concurrent co-planar forces $1N, 2N$ and $3N$ acting along different directions on a body

A

Can keep the body in equilibrium if $2N$ and $3N$ act at right angle

B

Can keep the body in equilibrium if $1N$ and $2N$ act at right angle

C

Cannot keep the body in equilibrium

D

Can keep the body in equilibrium if $1N$ and $3N$ act at an acute angle

Question 116: Palette 116/293

Errorless CBSE PMT 2009 MCQ

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

A

1 Mg / k

B

2 Mg / k

C

4 Mg / k

D

Mg / 2 k

Question 117: Palette 117/293

Errorless KCET 2009 MCQ

Two rectangular blocks $A$ and $B$ of masses $2\mathrm{kg}$ and $3\mathrm{kg}$ respectively are connected by a spring of spring constant $10.8Nm^{-1}$ and are placed on a frictionless horizontal surface. The block $A$ was given an initial velocity of 0.15 $ms^{-1}$ in the direction shown in the figure. The maximum compression of the spring during the motion is

A

0.01 m

B

0.02 m

C

0.05 m

D

0.03 m

Question 118: Palette 118/293

Errorless AMU (Engg.) 2009 MCQ

Two blocks of masses m and 2m are connected by a light string passing over a frictionless pulley. As shown in the figure, the mass m is placed on a smooth inclined plane of inclination $30^{\circ}$ and 2m hangs vertically. If the system is released, the blocks move with an acceleration equal to

A

$g / 4$

B

$g / 3$

C

g/2

D

g

Question 119: Palette 119/293

Errorless AMU PMT 2009 MCQ

Two bodies A and B of masses 10 kg and 15 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. If T represents the tension in the string when a horizontal force F = 500 N is applied to A (as shown in figure 1) and T' be the tension when it is applied to B (figure 2), then which of the following is true

A

$T = T' = 500N$

B

$T = T' = 250 N$

C

$T = 200N, T' = 300N$

D

$T = 300N, T' = 200N$

Question 120: Palette 120/293

Errorless DUMET 2009 MCQ

A rope of mass 0.1 kg is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At the contact point between the rope and the wall, the rope makes an angle $\theta = 10^{\circ}$ with respect to horizontal. The tension in the rope at its midpoint between the wall is

A

$2.78N$

B

$2.56N$

C

$2.82N$

D

$2.71N$

Question 121: Palette 121/293

Errorless MP PET 2009 MCQ

In a gravitational force field a particle is taken from A to B along different paths as shown in figure. Then

A

Work done along path I will be maximum

B

Work done along path III will be minimum

C

Work done along path IV will be minimum

D

Work done along all the paths will be the same

Question 122: Palette 122/293

Errorless DUMET 2009 MCQ

A block is lying static on the floor. The maximum value of static frictional force on the block is 10N. If a horizontal force of 8N is applied to the block, what will be the frictional force on the block

A

2N

B

18N

C

8N

D

10N

Question 123: Palette 123/293

Errorless MP PMT 2009, 10 MCQ

Which activity is not based upon friction

A

Writing

B

Speaking

C

Hearing

D

Walking

Question 124: Palette 124/293

Errorless DUMET 2009 MCQ

Two iron blocks of equal mass but with double surface area slide down an inclined plane with friction coefficient $\mu$ . If the first block with surface area $A$ experience a frictional force $f$ , then the second block with surface area $2A$ will experience a frictional force

A

$f / 2$

B

$f$

C

$2f$

D

$4f$

Question 125: Palette 125/293

Errorless IIT-JEE 2009 MCQ

A block of base $10 \, cm \times 10 \, cm$ and height $15 \, cm$ is kept on an inclined plane. The coefficient of friction between them is $\sqrt{3}$ . The inclination $\theta$ of this inclined plane from the horizontal plane is gradually increased from $0^\circ$ . Then

A

At $\theta = 30^\circ$ , the block will start sliding down the plane

B

The block will remain at rest on the plane up to certain $\theta$ and then it will topple

C

At $\theta = 60^\circ$ , the block will start sliding down the plane and continue to do so at higher angles

D

At $\theta = 60^\circ$ , the block will start sliding down the plane and on further increasing $\theta$ , it will topple at certain $\theta$

Question 126: Palette 126/293

Errorless KCET 2008 MCQ

A body of mass 4 kg is accelerated upon by a constant force, travels a distance of 5 m in the first second and a distance of 3 m in the third second. The force acting on the body is

A

6 N

B

8 N

C

2 N

D

4 N

Question 127: Palette 127/293

Errorless CBSE PMT 2008 MCQ

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be

A

$\frac{Mv}{2}$ newton

B

Zero

C

Mv newton

D

2 Mv newton

Question 128: Palette 128/293

Errorless J & K CET 2008 MCQ

The rate of mass of the gas emitted from rear of a rocket is initially 0.1 kg/sec. If the speed of the gas relative to the rocket is 50 m/sec and mass of the rocket is 2 kg, then the acceleration of the rocket in $m/sec^{2}$ is

A

5

B

5.2

C

2.5

D

25

Question 129: Palette 129/293

Errorless WB-JEE 2008 MCQ

A shell of mass 10 kg is moving with a velocity of $10 \, ms^{-1}$ when it blasts and forms two parts of mass 9 kg and 1 kg respectively. If the $1^{st}$ mass is stationary, the velocity of the $2^{nd}$ is

A

1 m/s

B

10 m/s

C

100 m/s

D

1000 m/s

Question 130: Palette 130/293

Errorless J & K CET 2008 MCQ

A gun fires N bullets per second, each of mass m with velocity v. The force exerted by the bullets on the gun is

A

vNm

B

$\frac{mv}{N}$

C

$mvN^{2}$

D

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

Question 131: Palette 131/293

Errorless WB-JEE 2008 MCQ

A rocket of mass 100 kg burns 0.1 kg of fuel per sec. If velocity of exhaust gas is 1 km/sec, then it lifts with an acceleration of

A

$1000 \, ms^{-2}$

B

$100 \, ms^{-2}$

C

$10 \, ms^{-2}$

D

$1 \, ms^{-2}$

Question 132: Palette 132/293

Errorless AIEEE 2008 MCQ

A body of mass $m = 3.513 \, \text{kg}$ is moving along the $x$ -axis with a speed of $5.00 \, \text{ms}^{-1}$ . The magnitude of its momentum is recorded as

A

$17.565 \, \text{kg} \, \text{ms}^{-1}$

B

$17.56 \, \text{kg} \, \text{ms}^{-1}$

C

$17.57 \, \text{kg} \, \text{ms}^{-1}$

D

$17.6 \, \text{kg} \, \text{ms}^{-1}$

Question 133: Palette 133/293

Errorless Odisha JEE 2008 MCQ

A body of mass 1000 kg is moving horizontally with a velocity 50 m/s. A mass of 250 kg is added. Find the final velocity

A

40 m/s

B

20 m/s

C

$30\sqrt{2}$ m/s

D

50 m/s

Question 134: Palette 134/293

Errorless Odisha JEE 2008 MCQ

A body shown in figure is accelerating downward with acceleration $2 \, m/s^{2}$ . The tension in the string is

A

$48N$

B

$50N$

C

30 N

D

42 N

Question 135: Palette 135/293

Errorless Kerala PMT 2008; WB-JEE 2010; MP PET 2012 MCQ

Two block of masses 7 kg and 5 kg are placed in contact with each other on a smooth surface. If a force of 6 N is applied on the heavier mass, the force on the lighter mass is

A

$3.5N$

B

2.5N

C

7 N

D

$5N$

E

6N

Question 136: Palette 136/293

Errorless Kerala PET 2008 MCQ

A particle of mass $2\mathrm{kg}$ is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below The velocity of the particle after 10 s is

A

$20ms^{-1}$

B

$10ms^{-1}$

C

75 ms $^{-1}$

D

$26ms^{-1}$

E

50 ms $^{-1}$

Question 137: Palette 137/293

Errorless Odisha JEE 2008 MCQ

A force of 20 N is applied on a body of mass 5 kg resting on a horizontal plane. The body gains a kinetic energy of 10 joule after it moves a distance 2 m. The frictional force is

A

10 N

B

15 N

C

20 N

D

30 N

Question 138: Palette 138/293

Errorless WB-JEE 2008 MCQ

Force required to move a mass of 1 kg at rest on a horizontal rough plane ( $\mu = 0.1$ and $g = 9.8 \, m/s^{2}$ ) is

A

0.98 N

B

0.49 N

C

9.8 N

D

4.9 N

Question 139: Palette 139/293

Errorless Odisha JEE 2008 MCQ

Two blocks, 4 kg and 2 kg are sliding down an incline plane as shown in figure. The acceleration of 2 kg block is

A

$1.6 6 m / s ^ {2}$

B

$2.6 6 m / s ^ {2}$

C

$3.6 6 m / s ^ {2}$

D

$4.6 6 m / s ^ {2}$

Question 140: Palette 140/293

Errorless AIIMS 2008 MCQ

Assertion : The velocity of a body at the bottom of an inclined plane of given height is more when it slides down the plane, compared to, when it rolling down the same plane. Reason : In rolling down a body acquires both, kinetic energy of translation and rotation.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 141: Palette 141/293

Errorless AIIMS 2008 MCQ

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

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 142: Palette 142/293

Errorless Kerala PMT 2007 MCQ

When a bullet is fired at a target, its velocity decreases by half after penetrating 30 cm into it. The additional thickness it will penetrate before coming to rest is

A

30 cm

B

40 cm

C

10 cm

D

50 cm

Question 143: Palette 143/293

Errorless Kerala PET 2007 MCQ

A shell at rest at the origin explodes into three fragments of masses 1kg, 2kg and m kg. The 1kg and 2kg pieces fly off with speeds of $5ms^{-1}$ along x-axis and $6ms^{-1}$ along y-axis respectively. If the m kg piece flies off with a speed of $6.5ms^{-1}$ , the total mass of the shell must be

A

4 kg

B

5 kg

C

3.5 kg

D

4.5 kg

Question 144: Palette 144/293

Errorless Kerala PET 2007 MCQ

A mass of 5kg is suspended by a rope of length 2m from a ceiling. A force of 50N in the horizontal direction is applied at the mid-point of the rope. The angle made by the rope with the vertical, in equilibrium is

A

50°

B

60°

C

30°

D

45°

Question 145: Palette 145/293

Errorless AIEEE 2007 MCQ

A block of mass ‘m’ is connected to another block of mass ‘M’ by a spring (massless) of spring constant ‘k’. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force ‘F’ starts acting on the block of mass ‘M’ to pull it. Find the force on the block of mass ‘m’

A

$\frac{mF}{M}$

B

$\frac{(M+mF)}{m}$

C

$\frac{mF}{(m+M)}$

D

$\frac{MF}{(m+M)}$

Question 146: Palette 146/293

Errorless IIT-JEE 2007 MCQ

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when them becomes 2x, is magnitude of acceleration, when the separation between them becomes 2x, is

A

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

B

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

C

$\frac{F}{2m}\frac{x}{a}$

D

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

Question 147: Palette 147/293

Errorless CBSE PMT 2007 MCQ

A block B is pushed momentarily along a horizontal surface with an initial velocity V. If $\mu$ is the coefficient of sliding friction between B and the surface, block B will come to rest after a time ____

A

$V / (g\mu)$

B

$g\mu /V$

C

$g / V$

D

$V / g$

Question 148: Palette 148/293

Errorless AIIMS 2007 MCQ

Assertion : The acceleration of a body down a rough inclined plane is greater than the acceleration due to gravity. Reason : The body is able to slide on a inclined plane only when its acceleration is greater than acceleration due to gravity.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 149: Palette 149/293

Errorless AFMC 2006 MCQ

A reference frame attached to the earth

A

Is an inertial frame by definition

B

Cannot be an inertial frame because earth is revolving round the sun

C

Is an inertial frame because Newton's laws are applicable

D

Is an inertial frame because the earth is rotating about its own axis

Question 150: Palette 150/293

Errorless Kerala PMT 2006 MCQ

Same force acts on two bodies of different masses 3 kg and 5 kg initially at rest. The ratio of times required to acquire same final velocity is

A

5:3

B

25:9

C

9:25

D

3:5

Question 151: Palette 151/293

Errorless KCET 2006 MCQ

For ordinary terrestrial experiments, the observer is an inertial frame in the following cases is

A

A child revolving in a giant wheel

B

A driver in a sports car moving with a constant high speed of $200\mathrm{kmh}^{-1}$ on a straight rod

C

The pilot of an aeroplane which is taking off

D

A cyclist negotiating a sharp curve

Question 152: Palette 152/293

Errorless J & K CET 2006 MCQ

Which of the following quantities measured from different inertial reference frames are same

A

Force

B

Velocity

C

Displacement

D

Kinetic energy

Question 153: Palette 153/293

Errorless J & K CET 2006; Kerala PMT 2009 MCQ

A large force is acting on a body for a short time. The impulse imparted is equal to the change in

A

Acceleration

B

Momentum

C

Energy

D

Velocity

E

Displacement

Question 154: Palette 154/293

Errorless BHU 2006 MCQ

In the first second of its flight, rocket ejects 1/60 of its mass with a velocity of $2400~\mathrm{ms}^{-1}$ . The acceleration of the rocket is

A

$19.6~\mathrm{ms}^{-2}$

B

$30.2~\mathrm{ms}^{-2}$

C

$40~\mathrm{ms}^{-2}$

D

$49.8~\mathrm{ms}^{-2}$

Question 155: Palette 155/293

Errorless UP CPMT 2006 MCQ

An object is kept on a smooth inclined plane of 1 in l. The horizontal acceleration to be imparted to the inclined plane so that the object is stationary relative to the inclined is

A

$g\sqrt{l^{2}-1}$

B

$g(l^{2}-1)$

C

$\frac{g}{\sqrt{l^{2}-1}}$

D

$\frac{g}{l^{2}-1}$

Question 156: Palette 156/293

Errorless IIT-JEE 2006; NEET 2017 MCQ

Two blocks A and B of masses 2m and m, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively

A

g, g/2

B

g/2, g

C

g, g

D

g/2, g/2

Question 157: Palette 157/293

Errorless DCE 2006 MCQ

A block of mass $M$ is attached to the lower end of a vertical rope of mass $m$ . An upward force $P$ acts on the upper end of the rope. The system is free to move. The force exerted by the rope on the block is $\frac{PM}{M + m}$

A

In all cases

B

Only if the rope is uniform

C

In gravity-free space only

D

Only if $P > (M + m)g$

Question 158: Palette 158/293

Errorless DCE 2006 MCQ

In the arrangement shown, the pulleys are fixed and ideal, the strings are light, $m_{1} > m_{2}$ and $S$ is a spring balance which is itself massless. The reading of $S$ (in unit of mass) is

A

$m _ {1} - m _ {2}$

B

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

C

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

D

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

Question 159: Palette 159/293

Errorless AIIMS 2006 MCQ

If a street light of mass $M$ is suspended from the end of a uniform rod of length $L$ in different possible patterns as shown in figure, then (A) (B) (C)

A

Pattern A is sturdier

B

Pattern B is sturdier

C

Pattern C is sturdier

D

All will have same sturdiness

Question 160: Palette 160/293

Errorless AIIMS 2006 MCQ

A person used force (F), shown in figure to move a load with constant velocity on given surface Identify the correct surface profile

A

B

C

D

Question 161: Palette 161/293

Errorless AIIMS 2006 MCQ

Assertion : A man in a closed cabin falling freely does not experience gravity. Reason : Inertial and gravitational mass have equivalence.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 162: Palette 162/293

Errorless MP PMT 2006 MCQ

A block weighing $W$ is held against a vertical wall by applying a horizontal force $F$ . The minimum value of $F$ needed to hold the block is

A

Less than $W$

B

Equal to $W$

C

Greater than $W$

D

Data is insufficient

Question 163: Palette 163/293

Errorless MP PET 2006; JEE (Main) 2018 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. The coefficient of static friction of A with table is 0.2. The minimum mass of C that may be placed on A to prevent it from moving is

A

15 kg

B

10 kg

C

5 kg

D

12 kg

Question 164: Palette 164/293

Errorless BHU 2006 MCQ

A body moves along a circular path of radius 10m and the coefficient of friction is 0.5. What should be its angular speed in rad/s if it is not to slip from the surface (g=9.8 ms²)

A

5

B

10

C

0.1

D

0.7

Question 165: Palette 165/293

Errorless IIT-JEE 2006 MCQ

A circular disc with a groove along its diameter is placed horizontally. A block of mass 1kg is placed as shown. The co-efficient of friction between the block and all surfaces of groove in contact is $\mu=2/5$ . The disc has an acceleration of $25\ m/s^{2}$ . Find the acceleration of the block with respect to disc $\cos \theta = 4 / 5$ $\sin \theta = 3 / 5$

A

$10 \, m/s^{2}$

B

$5m / s^2$

C

20 m/s²

D

$1m / s^2$

Question 166: Palette 166/293

Errorless AIIMS 2006 MCQ

Assertion : Use of ball bearings between two moving parts of machine is a common practice. Reason : Ball bearings reduce vibrations and provide good stability.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 167: Palette 167/293

Errorless BCECE 2005 MCQ

A ball of mass m moves with speed v and it strikes normally with a wall and reflected back normally, if its time of contact with wall is t then find force exerted by ball on wall

A

$\frac{2mv}{t}$

B

$\frac{mv}{t}$

C

$mut$

D

$\frac{mv}{2t}$

Question 168: Palette 168/293

Errorless KCET 2005 MCQ

The adjacent figure is the part of a horizontally stretched net. section AB is stretched with a force of 10 N. The tensions in the sections BC and BF are |E

A

10N, 11N

B

10N, 6N

C

10N, 10N

D

Can't calculate due to insufficient data

Question 169: Palette 169/293

Errorless AIEEE 2005; BCECE 2006 MCQ

A particle of mass 0.3 kg is subjected to a force F = -kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin

A

$5 \, m/s^{2}$

B

$10 \, m/s^{2}$

C

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

D

$15 \, m/s^{2}$

Question 170: Palette 170/293

Errorless RPMT 2005 MCQ

The mass of ship is $2 \times 10^{7}$ kg. On applying a force of $25 \times 10^{5}$ N, it is displaced through 25 m. After the displacement, the velocity acquired by the ship will be

A

12.5 m/s

B

5 m/s

C

3.7 m/s

D

2.5 m/s

Question 171: Palette 171/293

Errorless RPMT 2005 MCQ

A sphere is accelerated upwards by a cord whose braking strength is four times its weight. The maximum acceleration with which the sphere can move up without breaking the cord is

A

$g$

B

$3g$

C

$2g$

D

$4g$

Question 172: Palette 172/293

Errorless J & K CET 2005 MCQ

A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore

A

By throwing his shirt in vertically upward direction

B

By spitting horizontally

C

He will wait for the ice to melt in pond

D

Unable to get at the shore

Question 173: Palette 173/293

Errorless KCET 2005 MCQ

A student attempts to pull himself up by tugging on his hair. He will not succeed

A

As the force exerted is small

B

The frictional force while gripping, is small.

C

Newton's law of inertia is not applicable to living beings

D

As the force applied is internal to the system

Question 174: Palette 174/293

Errorless Kerala PMT 2005 MCQ

A book is lying on the table. What is the angle between the action of the book on the table and the reaction of the table on the book

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$180^{\circ}$

Question 175: Palette 175/293

Errorless Odisha JEE 2005 MCQ

For a body moving with relativistic speed, if the velocity is doubled, then

A

Its linear momentum is doubled

B

Its linear momentum will be less than double

C

Its linear momentum will be more than double

D

Its linear momentum remains unchanged

Question 176: Palette 176/293

Errorless AIEEE 2005; NEET 2018 MCQ

A block is kept on a frictionless inclined surface with angle of inclination ' $\alpha'$ . The incline is given an acceleration 'a' to keep the block stationary. Then a is equal to

A

g

B

$g\tan \alpha$

C

$g / \tan \alpha$

D

$g\csc \alpha$

Question 177: Palette 177/293

Errorless AIIMS 2005; AMU (Engg.) 2012 MCQ

In the figure given below, the position-time graph of a particle of mass 0.1 kg is shown. The impulse at t = 2 sec is

A

0.2 kg m sec $^{-1}$

B

$-0.2\mathrm{kg}m\sec^{-1}$

C

0.1 kg m sec $^{-1}$

D

-0.4 kg m sec $^{-1}$

Question 178: Palette 178/293

Errorless CBSE PMT 2004 MCQ

A block of mass m is placed on a smooth wedge of inclination $\theta$ . The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be

A

mg cos $\theta$

B

mg sin $\theta$

C

mg

D

mg / cos $\theta$

Question 179: Palette 179/293

Errorless Pb. PET 2004 MCQ

When a horse pulls a wagon, the force that causes the horse to move forward is the force

A

The ground exerts on it

B

It exerts on the ground

C

The wagon exerts on it

D

It exerts on the wagon

Question 180: Palette 180/293

Errorless Kerala PMT 2004 MCQ

An aircraft is moving with a velocity of $300ms^{-1}$ . If all the forces acting on it are balanced, then

A

It still moves with the same velocity

B

It will be just floating at the same point in space

C

It will fall down instantaneously

D

It will lose its velocity gradually

E

It will explode

Question 181: Palette 181/293

Errorless AIEEE 2004; Kerala PMT 2007 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 he fire per second at the most

A

One

B

Four

C

Two

D

Three

Question 182: Palette 182/293

Errorless DCE 2004 MCQ

If two forces of $5N$ each are acting along $X$ and $Y$ axes, then the magnitude and direction of resultant is

A

$5\sqrt{2}, \pi/3$

B

$5\sqrt{2}, \pi/4$

C

$-5\sqrt{2}, \pi/3$

D

$-5\sqrt{2}, \pi/4$

Question 183: Palette 183/293

Errorless DPMT 2004 MCQ

A lift is moving downwards with an acceleration equal to acceleration due to gravity. A body of mass m kept on the floor of the lift is pulled horizontally. If the coefficient of friction is $\mu$ , then the frictional resistance offered by the body is

A

mg

B

$\mu$ mg

C

2 $\mu$ mg

D

Zero

Question 184: Palette 184/293

Errorless CBSE PMT 2004; Odisha PMT 2004 MCQ

The coefficient of static friction, $\mu_{s}$ , between block $A$ of mass $2\mathrm{kg}$ and the table as shown in the figure is 0.2. What would be the maximum mass value of block $B$ so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless ( $g = 10m / s^2$ )

A

2.0 kg

B

4.0 kg

C

0.2 kg

D

0.4 kg

Question 185: Palette 185/293

Errorless MP PMT 2004 MCQ

A block of mass M=5 kg is resting on a rough horizontal surface for which the coefficient of friction is 0.2. When a force F=40 N is applied, the acceleration of the block will be $(g=10\ ms^{2})$

A

$5.7 3 \mathrm{m} / \mathrm{sec} ^ {2}$

B

$8.0 \mathrm{m} / \sec^ {2}$

C

$3.1 7 m / \sec^ {2}$

D

$1 0. 0 m / \sec^ {2}$

Question 186: Palette 186/293

Errorless AIEEE 2004; KCET 2018 MCQ

A block rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take $g = 10 \, m/s^{2}$ )

A

2.0

B

4.0

C

1.6

D

2.5

Question 187: Palette 187/293

Errorless J & K CET 2004 MCQ

A block of mass 2 kg rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is

A

$9.8N$

B

$0.7 \times 9.8 \times \sqrt{3} N$

C

$9.8 \times \sqrt{3} N$

D

$0.8 \times 9.8N$

Question 188: Palette 188/293

Errorless BHU 2004 MCQ

A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is $\mu$ . If the mass is pulled by a force P as shown in the figure, the limiting friction between body and surface will be

A

$\mu mg$

B

$\mu \left[mg + \left(\frac{P}{2}\right)\right]$

C

$\mu \left[mg - \left(\frac{P}{2}\right)\right]$

D

$\mu\left[mg-\left(\frac{\sqrt{3}P}{2}\right)\right]$

Question 189: Palette 189/293

Errorless IIT-JEE (Screening) 2004 MCQ

A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. $\mu_{s}$ is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is

A

kA

B

$\frac{kA}{2}$

C

Zero

D

$\mu_{s}mg$

Question 190: Palette 190/293

Errorless MP PMT 2003 MCQ

If a bullet of mass 5 gm moving with velocity 100 m/sec, penetrates the wooden block upto 6 cm. Then the average force imposed by the bullet on the block is

A

8300 N

B

417 N

C

830 N

D

Zero

Question 191: Palette 191/293

Errorless CBSE PMT 2003 MCQ

A monkey of mass 20kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the rope (g=10 m/s²)

A

10 m/s²

B

25 m/s²

C

2.5 m/s²

D

5 m/s²

Question 192: Palette 192/293

Errorless Odisha JEE 2003 MCQ

A plumb line is suspended from a ceiling of a car moving with horizontal acceleration of $a$ . What will be the angle of inclination with vertical

A

$\tan^{-1}(a / g)$

B

$\tan^{-1}(g / a)$

C

$\cos^{-1}(a / g)$

D

$\cos^{-1}(g / a)$

Question 193: Palette 193/293

Errorless UPSEAT 2003 MCQ

If in a stationary lift, a man is standing with a bucket full of water, having a hole at its bottom. The rate of flow of water through this hole is $R_{0}$ . If the lift starts to move up and down with same acceleration and then that rates of flow of water are $R_{u}$ and $R_{d}$ , then

A

$R_{0} > R_{u} > R_{d}$

B

$R_{u} > R_{0} > R_{d}$

C

$R_{d} > R_{0} > R_{u}$

D

$R_{u} > R_{d} > R_{0}$

Question 194: Palette 194/293

Errorless AIEEE 2003; RPET 2003; Kerala PMT 2003; RPMT 2005 MCQ

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of $5 \, m/s^{2}$ , the reading of the spring balance will be

A

49 N

B

24 N

C

74 N

D

15 N

Question 195: Palette 195/293

Errorless AIEEE 2003 MCQ

A light spring balance hangs from the hook of the other light spring balance and a block of mass $M$ kg hangs from the former one. Then the true statement about the scale reading is

A

Both the scales read $M / 2 \, \text{kg}$ each

B

Both the scales read $M \, \text{kg}$ each

C

The scale of the lower one reads $M \, \text{kg}$ and of the upper one zero

D

The reading of the two scales can be anything but the sum of the reading will be $M \, \text{kg}$

Question 196: Palette 196/293

Errorless AIEEE 2003 MCQ

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

A

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

B

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

C

$7.0 \times 10^{5} \, N$

D

$14.0 \times 10^{5} \, N$

Question 197: Palette 197/293

Errorless Odisha JEE 2003 MCQ

Which of the four arrangements in the figure correctly shows the vector addition of two forces $\overrightarrow{F_{1}}$ and $\overrightarrow{F_{2}}$ to yield the third force $\overrightarrow{F_{3}}$

A

B

C

D

Question 198: Palette 198/293

Errorless AIEEE 2003 MCQ

Three forces starts acting simultaneously on a particle moving with velocity $\vec{v}$ . These forces are represented in magnitude and direction by the three sides of a triangle ABC (as shown). The particle will now move with velocity

A

$\vec{v}$ remaining unchanged

B

Less than $\vec{v}$

C

Greater than $\vec{v}$

D

$\vec{v}$ in the direction of the largest force $BC$

Question 199: Palette 199/293

Errorless KCET 2003; UPSEAT 2004 MCQ

Which of the following groups of forces could be in equilibrium

A

3 N, 4 N, 5 N

B

4 N, 5 N, 10 N

C

30 N, 40 N, 80 N

D

1 N, 3 N, 5 N

Question 200: Palette 200/293

Errorless AIEEE 2003; Odisha JFE 2003; WB-JEE 2010 MCQ

A boy of mass 40 kg is climbing a vertical pole at a constant speed. If the coefficient of friction between his palms and the pole is 0.8 and $g = 10m/s^{2}$ , the horizontal force that he is applying on the pole is

A

300 N

B

400 N

C

500 N

D

600 N

Question 201: Palette 201/293

Errorless MP PMT 2003 MCQ

A block of 1 kg is stopped against a wall by applying a force F perpendicular to the wall. If $\mu = 0.2$ then minimum value of F will be

A

980 N

B

49 N

C

98 N

D

490 N

Question 202: Palette 202/293

Errorless BVP 2003; IIT-JEE 2008 MCQ

It is easier to roll a barrel than pull it along the road. This statement is

A

False

B

True

C

Uncertain

D

Not possible

Question 203: Palette 203/293

Errorless AIEEE 2003 MCQ

A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10s. Then the coefficient of friction is

A

0.01

B

0.02

C

0.03

D

0.06

Question 204: Palette 204/293

Errorless UPSEAT 2003 MCQ

A 2 kg mass starts from rest on an inclined smooth surface with inclination $30^{\circ}$ and length 2 m. How much will it travel before coming to rest on a frictional surface with frictional coefficient of 0.25

A

4 m

B

6 m

C

8 m

D

2 m

Question 205: Palette 205/293

Errorless IIT-JEE (Screening) 2003 MCQ

What is the maximum value of the force $F$ such that the block shown in the arrangement, does not move

A

$20N$

B

$10N$

C

$12N$

D

$15N$

Question 206: Palette 206/293

Errorless AIEEE 2002 MCQ

A lift is moving down with acceleration $a$ . A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively

A

$g, g$

B

$g - a, g - a$

C

$g - a, g$

D

$a, g$

Question 207: Palette 207/293

Errorless Pb. PET 2002 MCQ

The linear momentum p of a body moving in one dimension varies with time according to the equation $p = a + bt^{2}$ where a and b are positive constants. The net force acting on the body is

A

A constant

B

Proportional to $t^{2}$

C

Inversely proportional to t

D

Proportional to t

Question 208: Palette 208/293

Errorless AFMC 2002; MP PET 2002 MCQ

A force of 10 Newton acts on a body of mass $20\mathrm{kg}$ for 10 seconds. Change in its momentum is

A

$5\mathrm{kg}m / s$

B

$100\mathrm{kg}m / s$

C

$200\mathrm{kg}m / s$

D

$1000\mathrm{kg}m / s$

Question 209: Palette 209/293

Errorless Pb. PMT 2002 MCQ

A block of mass 5kg is moving horizontally at a speed of 1.5 m/s. A perpendicular force of 5N acts on it for 4 sec. What will be the distance of the block from the point where the force started acting

A

10 m

B

8 m

C

6 m

D

2 m

Question 210: Palette 210/293

Errorless KCET 2002 MCQ

The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is

A

$60^{\circ}$

B

$120^{\circ}$

C

$150^{\circ}$

D

$90^{\circ}$

Question 211: Palette 211/293

Errorless AIEEE 2002 MCQ

Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and magnitude of resultant is 12 N. Then the magnitudes of the forces are

A

12 N, 6 N

B

13 N, 5 N

C

10 N, 8 N

D

16 N, 2 N

Question 212: Palette 212/293

Errorless AIEEE 2002 MCQ

Which of the following is the correct order of forces

A

Weak < gravitational forces < strong forces (nuclear) < electrostatic

B

Gravitational $ < $ weak $ < $ (electrostatic) $ < $ strong force

C

Gravitational $ < $ electrostatic $ < $ weak $ < $ strong force

D

Weak < gravitational < electrostatic < strong forces

Question 213: Palette 213/293

Errorless Odisha JEE 2002 MCQ

Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force F = 10N, then tension $T_{1} =$

A

$1N$

B

$5N$

C

8N

D

$10N$

Question 214: Palette 214/293

Errorless Kerala PMT 2002 MCQ

A body of weight 2kg is suspended as shown in the figure. The tension $T_{1}$ in the horizontal string (in kg wt) is

A

$2 / \sqrt{3}$

B

$\sqrt{3} / 2$

C

$2\sqrt{3}$

D

2

Question 215: Palette 215/293

Errorless AIEEE 2002 MCQ

One end of a massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. with what value of minimum safe acceleration (in $ms^{-2}$ ) can a monkey of 60 kg move down on the rope

A

16

B

6

C

4

D

8

Question 216: Palette 216/293

Errorless AIEEE 2002 MCQ

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$ then the ratio of the masses is

A

8:1

B

9:7

C

4:3

D

5:3

Question 217: Palette 217/293

Errorless UPSEAT 2002 MCQ

A pulley fixed to the ceiling carries a string with blocks of mass $m$ and $3m$ attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with what acceleration

A

0

B

$g / 4$

C

$g / 2$

D

$-g / 2$

Question 218: Palette 218/293

Errorless AIEEE 2002 MCQ

When forces $F_{1}, F_{2}, F_{3}$ are acting on a particle of mass $m$ such that $F_{2}$ and $F_{3}$ are mutually perpendicular, then the particle remains stationary. If the force $F_{1}$ is now removed then the acceleration of the particle is

A

$F_{1}/m$

B

$F_{2}F_{3}/mF_{1}$

C

$(F_{2}-F_{3})/m$

D

$F_{2}/m$

Question 219: Palette 219/293

Errorless AIIMS 2002; BHU 2004 MCQ

If a ladder weighing 250 N is placed against a smooth vertical wall having coefficient of friction between it and floor is 0.3, then what is the maximum force of friction available at the point of contact between the ladder and the floor

A

75 N

B

50 N

C

35 N

D

25 N

Question 220: Palette 220/293

Errorless BHU 2002 MCQ

A car is moving along a straight horizontal road with a speed $v_{0}$ . If the coefficient of friction between the tyres and the road is $\mu$ , the shortest distance in which the car can be stopped is

A

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

B

$\frac{v_0}{\mu g}$

C

$\left(\frac{v_0}{\mu g}\right)^2$

D

$\frac{v_0}{\mu}$

Question 221: Palette 221/293

Errorless DPMT 2002 MCQ

Two carts of masses 200 kg and 300 kg on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails are same. If the 200 kg cart travels a distance of 36 m and stops, then the distance travelled by the cart weighing 300 kg is

A

32 m

B

24 m

C

16 m

D

12 m

Question 222: Palette 222/293

Errorless Pb. PMT 2002 MCQ

A fireman of mass 60 kg slides down a pole. He is pressing the pole with a force of 600 N. The coefficient of friction between the hands and the pole is 0.5, with what acceleration will the fireman slide down ( $g=10\ m/s^{2}$ )

A

$1\ m/s^{2}$

B

$2.5\ m/s^{2}$

C

$10\ m/s^{2}$

D

$5\ m/s^{2}$

Question 223: Palette 223/293

Errorless AIIMS 2002 MCQ

A block of mass 10 kg is placed on a rough horizontal surface having coefficient of friction $\mu = 0.5$ . If a horizontal force of 100 N is acting on it, then acceleration of the block will be

A

$0.5 \, m/s^{2}$

B

$5 \, m/s^{2}$

C

$10 \, m/s^{2}$

D

$15 \, m/s^{2}$

Question 224: Palette 224/293

Errorless JIPMER 2002; MP PET 2010 MCQ

A coin of mass 10g is placed over a book of length 50 cm. The coin is on the verge of sliding when one end of the book is lifted 10 cm up. The coefficient of static friction between the book and the coin is

A

1.0

B

0.4

C

0.3

D

0.2

Question 225: Palette 225/293

Errorless MP PMT 2002; CBSE PMT 2006; AFMC 2006 MCQ

300 Joule of work is done in sliding up a 2 kg block on an inclined plane to a height of 10 metres. Taking value of acceleration due to gravity 'g' to be 10 m/s², work done against friction is

A

100 J

B

200 J

C

300 J

D

Zero

Question 226: Palette 226/293

Errorless AFMC 2001 MCQ

A particle is moving with a constant speed along a straight line path. A force is not required to

A

Increase its speed

B

Decrease the momentum

C

Change the direction

D

Keep it moving with uniform velocity

Question 227: Palette 227/293

Errorless CBSE PMT 2001; BHU 2001; Kerala PET 2005; AIEEE 2006 MCQ

A player caught a cricket ball of mass 150 gm moving at the rate of 20 m/sec. If the catching process be completed in 0.1 sec the force of the blow exerted by the ball on the hands of player is

A

0.3 N

B

30 N

C

300 N

D

3000 N

Question 228: Palette 228/293

Errorless AIIMS 2001; Odisha JEE 2002; AMU (Engg.) 2012 MCQ

A gun fires a bullet of mass 50 g with a velocity of $30msec^{-1}$ . Because of this the gun is pushed back with a velocity of $1msec^{-1}$ . The mass of the gun is

A

15 kg

B

30 kg

C

1.5 kg

D

20 kg

Question 229: Palette 229/293

Errorless DPMT 2001; Pb. PMT 2002; MP PMT 2004; Odisha JEE 2005 MCQ

A diwali rocket is ejecting 0.05 kg of gases per second at a velocity of 400 m/sec. The accelerating force on the rocket is

A

20 dynes

B

20 N

C

22 dynes

D

1000 N

Question 230: Palette 230/293

Errorless IIT-JEE 2001 MCQ

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be

A

$0^{\circ}$

B

$30^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 231: Palette 231/293

Errorless IIT-JEE 2001 MCQ

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by

A

$\sqrt{2} Mg$

B

$\sqrt{2} mg$

C

$\sqrt{(M + m)^2 + m^2} g$

D

$\sqrt{(M + m)^2 + M^2} g$

Question 232: Palette 232/293

Errorless CBSE PMT 2001 MCQ

On the horizontal surface of a truck ( $\mu = 0.6$ ), a block of mass 1 kg is placed. If the truck is accelerating at the rate of $5m/sec^{2}$ then frictional force on the block will be

A

5 N

B

6 N

C

5.88 N

D

8 N

Question 233: Palette 233/293

Errorless CBSE PMT 2001; MP PMT 2009 MCQ

A vehicle of mass m is moving on a rough horizontal road with momentum P. If the coefficient of friction between the tyres and the road be $\mu$ , then the stopping distance is

A

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

B

$\frac{P^{2}}{2\mu mg}$

C

$\frac{P}{2\mu m^{2}g}$

D

$\frac{P^{2}}{2\mu m^{2}g}$

Question 234: Palette 234/293

Errorless EAMCET 2001 MCQ

A body of weight 64 N is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are 0.6 and 0.4 respectively, the acceleration of the body will be (Acceleration due to gravity = g)

A

$\frac{g}{6.4}$

B

0.64 g

C

$\frac{g}{32}$

D

0.2 g

Question 235: Palette 235/293

Errorless IIT-JEE 2001 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

$\operatorname{cosec} \alpha = 3$

Question 236: Palette 236/293

Errorless EAMCET (Med.) 2000; Odisha JEE 2008 MCQ

A gun of mass 10kg fires 4 bullets per second. The mass of each bullet is 20 g and the velocity of the bullet when it leaves the gun is 300 ms $^{-1}$ . The force required to hold the gun while firing is

A

6 N

B

8 N

C

24 N

D

240 N

Question 237: Palette 237/293

Errorless CBSE PMT 2000; Odisha JEE 2002; AIEEE 2004; Kerala PET 2005 MCQ

Two masses of 5kg and 10kg are connected to a pulley as shown. What will be the acceleration of the system (g = acceleration due to gravity)

A

g

B

$\frac{g}{2}$

C

$\frac{g}{3}$

D

$\frac{g}{4}$

Question 238: Palette 238/293

Errorless AMU (Engg.) 2000; Kerala PET 2010 MCQ

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force F applied on the upper string produces an acceleration of $2m/s^{2}$ in the upward direction in both the blocks. If T and $T'$ be the tensions in the two parts of the string, then $(g = 9.8\ m/s^{2})$

A

T = 70.8N and $T' = 47.2N$

B

T = 58.8N and $T' = 47.2N$

C

T = 70.8N and $T' = 58.8N$

D

T = 70.8N and $T' = 0$

Question 239: Palette 239/293

Errorless MP PET 2000;J & K CET 2006; Odisha JEE 2009 MCQ

A block of mass 2 kg is kept on the floor. The coefficient of static friction is 0.4. If a force F of 2.5 Newtons is applied on the block as shown in the figure, the frictional force between the block and the floor will be

A

2.5N

B

5N

C

7.84N

D

10N

Question 240: Palette 240/293

Errorless Pb. PMT 2000; NEET 2013 MCQ

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

A

$\mu = \sin \theta$

B

$\mu = \cot \theta$

C

$\mu = 2\cos \theta$

D

$\mu = 2\tan \theta$

Question 241: Palette 241/293

Errorless JIPMER 2000; Kerala PET 2009 MCQ

A body of mass 10 kg is lying on a rough plane inclined at an angle of $30^{\circ}$ to the horizontal and the coefficient of friction is 0.5. The minimum force required to pull the body up the plane is

A

914 N

B

91.4 N

C

9.14 N

D

0.914 N

Question 242: Palette 242/293

Errorless AFMC 1999; CPMT 2000, 01 MCQ

When a bus suddenly takes a turn, the passengers are thrown outwards because of

A

Inertia of direction

B

Acceleration of motion

C

Speed of motion

D

Both

Question 243: Palette 243/293

Errorless AFMC 1999; CBSE PMT 2000; CPMT 2001; DPMT 2003 MCQ

The average force necessary to stop a bullet of mass 20 g moving with a speed of 250 m/s, as it penetrates into the wood for a distance of 12 cm is

A

$2.2 \times 10^{3} N$

B

$3.2 \times 10^{3} N$

C

$4.2 \times 10^{3} N$

D

$5.2 \times 10^{3} N$

Question 244: Palette 244/293

Errorless AFMC 1999; Pb. PMT 2003 MCQ

A ball of mass 150g starts moving with an acceleration of $20m/s^{2}$ . When hit by a force, which acts on it for 0.1 sec the impulsive force is

A

0.5 N-s

B

0.1 N-s

C

0.3 N-s

D

1.2 N-s

Question 245: Palette 245/293

Errorless CBSE PMT 1999; MH CET 2003; Pb. PMT 2004 MCQ

If force on a rocket having exhaust velocity of 300 m/sec is 210 N, then rate of combustion of the fuel is

A

0.7 kg/s

B

1.4 kg/s

C

0.07 kg/s

D

10.7 kg/s

Question 246: Palette 246/293

Errorless BHU 1999; BCECE 2004 MCQ

To avoid slipping while walking on ice, one should take smaller steps because of the

A

Friction of ice is large

B

Larger normal reaction

C

Friction of ice is small

D

Smaller normal reaction

Question 247: Palette 247/293

Errorless MP PMT 1999; Pb. PMT 2001, 04; AIEEE 2005; CBSE PMT (Mains) 2011; MP PET 2013 MCQ

Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of kinetic friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is $[g = 10 \, ms^{-2}]$

A

30 m

B

40 m

C

72 m

D

20 m

Question 248: Palette 248/293

Errorless CBSE PMT 1999, 2000; AIIMS 2000; BHU 2001 MCQ

A block of mass 50 kg slides over a horizontal distance of 1 m. If the coefficient of friction between their surfaces is 0.2, then work done against friction is

A

98 J

B

72 J

C

56 J

D

34 J

Question 249: Palette 249/293

Errorless JIPMER 1999; RPET 1999; AMU 2000; Kerala PMT 2006; AIIMS 2008; JEE (Main Online) 2018 MCQ

A given object takes n times as much time to slide down a $45^{\circ}$ rough incline as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is given by

A

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

B

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

C

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

D

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

Question 250: Palette 250/293

Errorless MP PMT/PET 1998; RPET 2001; BHU 2001; MP PMT 2003 MCQ

n small balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will be

A

mnu

B

2 mnu

C

4 mnu

D

$\frac{1}{2} mnu$

Question 251: Palette 251/293

Errorless AFMC 1998, 2003 MCQ

Swimming is possible on account of

A

First law of motion

B

Second law of motion

C

Third law of motion

D

Newton's law of gravitation

Question 252: Palette 252/293

Errorless CBSE PMT 1998; Odisha JEE 2009 MCQ

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

A

$127.5 kg s^{-1}$

B

$187.5 kg s^{-1}$

C

$185.5 kg s^{-1}$

D

$137.5 kg s^{-1}$

Question 253: Palette 253/293

Errorless AIIMS 1998; JIPMER 2001, 02 MCQ

Rocket engines lift a rocket from the earth surface because hot gas with high velocity

A

Push against the earth

B

Push against the air

C

React against the rocket and push it up

D

Heat up the air which lifts the rocket

Question 254: Palette 254/293

Errorless MP PMT/PET 1998; Odisha JEE 2008 MCQ

Three blocks of masses $m_{1}, m_{2}$ and $m_{3}$ are connected by massless strings as shown on a frictionless table. They are pulled with a force $T_{3} = 40 N$ . If $m_{1} = 10 kg, m_{2} = 6 kg$ and $m_{3} = 4 kg$ , the tension $T_{2}$ will be

A

$20N$

B

$40N$

C

$10N$

D

$32N$

Question 255: Palette 255/293

Errorless AFMC 1998 MCQ

A force of 50 dynes is acted on a body of mass $5g$ which is at rest for an interval of 3 seconds, then impulse is

A

$0.15 \times 10^{-3} N$ -s

B

$0.98 \times 10^{-3} N$ -s

C

$1.5 \times 10^{-3} N$ -s

D

$2.5 \times 10^{-3} N$ -s

Question 256: Palette 256/293

Errorless AFMC 1998, 99; AIIMS 2001 MCQ

When two surfaces are coated with a lubricant, then they

A

Stick to each other

B

Slide upon each other

C

Roll upon each other

D

None of these

Question 257: Palette 257/293

Errorless CPMT 1997; CBSE PMT 2006 MCQ

A 100 g iron ball having velocity 10 m/s collides with a wall at an angle $30^{\circ}$ and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the wall is

A

10 N

B

100 N

C

1.0 N

D

0.1 N

Question 258: Palette 258/293

Errorless RPET 1997; RPMT 2005; BHU 2006 MCQ

The coefficient of friction between a body and the surface of an inclined plane at $45^{\circ}$ is 0.5. If $g = 9.8 \, m/s^{2}$ , the acceleration of the body downwards in $m/s^{2}$ is

A

$\frac{4.9}{\sqrt{2}}$

B

$4.9\sqrt{2}$

C

$19.6\sqrt{2}$

D

4.9

Question 259: Palette 259/293

Errorless CBSE PMT 1996, 2009; Odisha JEE 2011 MCQ

A force vector applied on a mass is represented as $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k}$ and accelerates with $1m / s^2$ . What will be the mass of the body

A

$10\sqrt{2} kg$

B

$2\sqrt{10} kg$

C

$10kg$

D

$20kg$

Question 260: Palette 260/293

Errorless MP PMT 1996; AIEEE 2003 MCQ

A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block will be

A

P

B

$\frac{Pm}{M+m}$

C

$\frac{PM}{M+m}$

D

$\frac{Pm}{M-m}$

Question 261: Palette 261/293

Errorless RPET 1996; JIPMER 2001, 02; AMU (Engg.) 2010 MCQ

A light string passes over a frictionless pulley. To one of its ends a mass of 6 kg is attached. To its other end a mass of 10 kg is attached. The tension in the thread will be

A

$24.5N$

B

2.45 N

C

79 N

D

73.5 N

Question 262: Palette 262/293

Errorless Manipal MEE 1995; MP PMT 1999, 2000; DCE 2000, 03, 09; Pb. PMT 2001, 04; CBSE PMT 2002, 03, 09; Kerala PET 2002, 08; DPMT 2003; Odisha JEE 2011; CBSE PMT (Pre.) 2011 MCQ

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button one control panel. The lift starts moving upwards with an acceleration $1.0 \, m/s^{2}$ . If $g = 10 \, ms^{-2}$ , the tension in the supporting cable is

A

1200 N

B

8600 N

C

9680 N

D

11000 N

Question 263: Palette 263/293

Errorless MP PMT 1995; BVP 2003 MCQ

A boy having a mass equal to 40 kilograms is standing in an elevator. The force felt by the feet of the boy will be greatest when the elevator $(g = 9.8 \text{ metres} / \text{sec}^2)$

A

Stands still

B

Moves downward at a constant velocity of 4 metres/sec

C

Accelerates downward with an acceleration equal to $4 \, metres/sec^{2}$

D

Accelerates upward with an acceleration equal to $4 \, metres/sec^{2}$

Question 264: Palette 264/293

Errorless EAMCET (Med.) 1995; Pb. PMT 1999; KCET 2000; MP PET 2002 MCQ

A body of mass 1.0kg is falling with an acceleration of 10 m/sec $^{2}$ . Its apparent weight will be (g = 10m/sec $^{2}$ )

A

1.0kg wt

B

2.0kg wt

C

0.5kg wt

D

Zero

Question 265: Palette 265/293

Errorless Manipal MEE 1995; MP PMT 2010 MCQ

Newton's third law of motion leads to the law of conservation of

A

Angular momentum

B

Energy

C

Mass

D

Momentum

Question 266: Palette 266/293

Errorless AFMC 1995; CBSE PMT 1996; JIPMER 1999, 2000 Pb. PMT 2002; DCE 2004 MCQ

A man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of one kg mass. By what velocity the gun rebounds backwards

A

0.1 m/s

B

10 m/s

C

1 m/s

D

0.01 m/s

Question 267: Palette 267/293

Errorless EAMCET (Engg.) 1995; Kerala PET 2005 MCQ

A uniform metal chain is placed on a rough table such that one end of chain hangs down over the edge of the table. When one-third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is

A

$\frac{3}{4}$

B

$\frac{1}{4}$

C

$\frac{2}{3}$

D

$\frac{1}{2}$

Question 268: Palette 268/293

Errorless AMU 1995; MH CET (Med.) 1999, 2001; Kerala PET 2007; MP PET 2013 MCQ

The maximum speed of a car on a road turn of radius 30m; if the coefficient of friction between the tyres and the road is 0.4; will be

A

9.84 m/s

B

10.84 m/s

C

7.84 m/s

D

5.84 m/s

Question 269: Palette 269/293

Errorless SCRA 1994 MCQ

A person is sitting in a travelling train and facing the engine. He tosses up a coin and the coin falls behind him. It can be concluded that the train is

A

Moving forward and gaining speed

B

Moving forward and losing speed

C

Moving forward with uniform speed

D

Moving backward with uniform speed

Question 270: Palette 270/293

Errorless MCQ

A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2m while applying the force and the ball goes up to 2m height further, find the magnitude of the force. Consider $g = 10m/s^{2}$

A

16 N

B

20 N

C

22 N

D

4 N

Question 271: Palette 271/293

Errorless MCQ

Assertion : Inertia is the property by virtue of which the body is unable to change by itself the state of rest only. Reason : The bodies do not change their state unless acted upon by an unbalanced external force.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 272: Palette 272/293

Errorless MCQ

Assertion : If the net external force on the body is zero, then its acceleration is zero. Reason : Acceleration does not depend on force.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 273: Palette 273/293

Errorless MCQ

Assertion : Force is required to move a body uniformly along a circle. Reason : When the motion is uniform, acceleration is zero.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 274: Palette 274/293

Errorless MCQ

Assertion : A body subjected to three concurrent forces cannot be in equilibrium. Reason : If large number of concurrent forces acting on the same point, then the point will be in equilibrium, if sum of all the forces is equal to zero.

A

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

B

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

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 275: Palette 275/293

Errorless MCQ

A car is moving with uniform velocity on a rough horizontal road. Therefore, according to Newton's first law of motion

A

No force is being applied by its engine

B

A force is surely being applied by its engine

C

An acceleration is being produced in the car

D

The kinetic energy of the car is increasing

Question 276: Palette 276/293

Errorless MCQ

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

A

$(g + a)\sin \theta$

B

$(g - a)$

C

$g\sin \theta$

D

$(g - a)\sin \theta$

Question 277: Palette 277/293

Errorless MCQ

A $60\mathrm{kg}$ man stands on a spring scale in the lift. At some instant he finds, scale reading has changed from $60\mathrm{kg}$ to $50\mathrm{kg}$ for a while and then comes back to the original mark. What should we conclude

A

The lift was in constant motion upwards

B

The lift was in constant motion downwards

C

The lift while in constant motion upwards, is stopped suddenly

D

The lift while in constant motion downwards, is suddenly stopped

Question 278: Palette 278/293

Errorless MCQ

Three weight $A, B$ and $C$ are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting $A$ and $B$ is (where $g$ is

A

g

B

$\frac{g}{9}$

C

$\frac{8g}{9}$

D

$\frac{10g}{9}$

Question 279: Palette 279/293

Errorless MCQ

The masses of 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, the 10 kg mass has acceleration $12 \, m/sec^{2}$ . What is the acceleration of 20 kg mass

A

$12m / \sec^2$

B

$4m / \sec^2$

C

$10m / \sec^2$

D

Zero

Question 280: Palette 280/293

Errorless MCQ

A spring balance and a physical balance are kept in a lift. In these balances equal masses are placed. If now the lift starts moving upwards with constant acceleration, then

A

The reading of spring balance will increase and the equilibrium position of the physical balance will disturb

B

The reading of spring balance will remain unchanged and physical balance will remain in equilibrium

C

The reading of spring balance will decrease and physical balance will remain in equilibrium

D

The reading of spring balance will increase and the physical balance will remain in equilibrium

Question 281: Palette 281/293

Errorless 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

$g(1 - 2\mu) / 3$

B

$g(1 - 2\mu) / 2$

C

$g(1 - g\mu) / 9$

D

$2g\mu /3$

Question 282: Palette 282/293

Errorless MCQ

Work done by a frictional force is

A

Negative

B

Positive

C

Zero

D

All of the above

Question 283: Palette 283/293

Errorless MCQ

The time taken by an object to slide down $45^{\circ}$ rough inclined plane is n times as it takes to slide down a perfectly smooth $45^{\circ}$ incline place. The coefficient of kinetic friction between the object and the incline plane is

A

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

B

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

C

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

D

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

Question 284: Palette 284/293

Errorless MCQ

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is $0.15(g = 10 \, m \, s^{-2})$

A

$150 \, m \, s^{-2}$

B

$1.5 \, m \, s^{-2}$

C

$50 \, m \, s^{-2}$

D

$1.2 \, m \, s^{-2}$

Question 285: Palette 285/293

Errorless MCQ

A force of 19.6 N when applied parallel to the surface just moves a body of mass 10 kg kept on a horizontal surface. If a 5 kg mass is kept on the first mass, the force applied parallel to the surface to just move the combined body is

A

29.4 N

B

39.2 N

C

18.6 N

D

42.6 N

Question 286: Palette 286/293

Errorless MCQ

If the normal force is doubled, the coefficient of friction is

A

Not changed

B

Halved

C

Doubled

D

Tripled

Question 287: Palette 287/293

Errorless MCQ

A body of weight 50 N placed on a horizontal surface is just moved by a force of 28.2 N. The frictional force and the normal reaction are

A

10N, 15N

B

20N, 30N

C

2N, 3N

D

5N, 6N

Question 288: Palette 288/293

Errorless MCQ

A rough vertical board has an acceleration 'a' so that a 2 kg block pressing against it does not fall. The coefficient of friction between the block and the board should be

A

$ > g / a$

B

$ < g / a$

C

= g/a

D

$>a / g$

Question 289: Palette 289/293

Errorless MCQ

A stone weighing 1 kg and sliding on ice with a velocity of 2 m/s is stopped by friction in 10 sec. The force of friction (assuming it to be constant) will be

A

-20 N

B

-0.2 N

C

0.2 N

D

20 N

Question 290: Palette 290/293

Errorless MCQ

A body of mass 10 kg slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt{3}$ . Taking $g = 10 \, m/s^{2}$ , the least force which acts at an angle of $30^{\circ}$ to the horizontal is

A

25 N

B

100 N

C

50 N

D

$\frac{50}{\sqrt{3}}N$

Question 291: Palette 291/293

Errorless MCQ

A child weighing 25 kg slides down a rope hanging from the branch of a tall tree. If the force of friction acting against him is 2 N, what is the acceleration of the child (Take $g = 9.8 \, m/s^{2}$ )

A

$22.5 \, m/s^{2}$

B

$8 \, m/s^{2}$

C

$5 \, m/s^{2}$

D

$9.72 \, m/s^{2}$

Question 292: Palette 292/293

Errorless MCQ

In the above question, if the lift is moving upwards with a uniform velocity, then the frictional resistance offered by the body is

A

$Mg$

B

$\mu Mg$

C

$2\mu Mg$

D

Zero

Question 293: Palette 293/293

Errorless MCQ

A body of mass 2 kg is moving on the ground comes to rest after some time. The coefficient of kinetic friction between the body and the ground is 0.2. The retardation in the body is

A

$9.8 \, m/s^{2}$

B

$4.73 \, m/s^{2}$

C

$2.16 \, m/s^{2}$

D

$1.96 \, m/s^{2}$