Master Resource Book in JEE Main Physics

D. B. Singh

Chapter 6

Laws of Motion and Friction - all with Video Answers

Educators

Section 1

Round 1

Problem 1

Two blocks are in contact on a frietionless table. One has mass $m$ and other $2 m$. A force $f$ is applied on $2 m$ as shown in flgure. Next the same force $F$ is applied from the right on $m$. In the two cases respectively, the force of contact between the two blocks will be
(a) $2: 1$
(b) $1: 3$
(c) $1: \underline{2}$
(d) $3: 1$

Raj Bala

Raj Bala

Numerade Educator

Problem 2

A ball of mass $0.2 \mathrm{~kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \mathrm{~m}$ while applying a force and the ball goes upto $2 \mathrm{~m}$ height further find, the magnitude of the force. Consider $g=10 \mathrm{~m} / \mathrm{s}^{2}$
[a) $16 \mathrm{~N}$
(b) $20 \mathrm{~N}$
(c) $22 \mathrm{~N}$
(d) $44 \mathrm{~N}$

Dheeraj Sharma

Numerade Educator

Problem 3

A wooden wedge of mass $M$ and inclination angle $\alpha$ rests on a smooth floor. A block of mass $m$ is kept on wedge. A force $P$ is applied on the wedge as shown in figure, such that a block remains stationary with respeet to wedge. The magnitude of force $\mathrm{P}$ is
(a) $(M+m) g \tan \alpha$
(b) $g \tan \alpha$
(c) $m g \cos \alpha$
(d) $(M+m) g \operatorname{cosec} \alpha$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 4

Conservation of momentum in a collision between particles can be understood from $\quad$ [NCERT Exemplar]
(a) conservation of energy
(b) Newton's first law only
(c) Newton's second law only
(d) both Newton's second and thind law

Narayan Hari

Numerade Educator

Problem 5

A body of mass $0.05 \mathrm{~kg}$ is obgerved to fall with an acceleration of $9.5 \mathrm{~ms}^{-2}$, The opposite force of air on the body is $\left(g=9.8 \mathrm{~ms}^{-2}\right)$
(a) $0.015 \mathrm{~N}$
(b) $0.15 \mathrm{~N}$
(c) $0.030 \mathrm{~N}$
(d) zero

Vysakh M

Numerade Educator

Problem 6

A rocket with a lift-off mass $20000 \mathrm{~kg}$ is blasted upwards with an initial acceleration of $5.0 \mathrm{~m} / \mathrm{s}^{2}$. Calculate the initial thrust (force) of the blast. [NCERT]
(a) $3 \times 10^{5} \mathrm{~N}$
(b) $2 \times 10^{8} \mathrm{~N}$
(c) $4 \times 10^{5} \mathrm{~N}$
(d) $5 \times 10^{5} \mathrm{~N}$

Dheeraj Sharma

Numerade Educator

Problem 7

A lift is moving upwards with a uniform velocity $v$ in which a block of mass $m$ is lying. The frictional force offered by the block, when coefficient of the frictional force is $\mu$, will be
(a) zero
(b) $m g$
(c) $\mu$ mg
(d) $2 \mu \overline{m g}$

Dheeraj Sharma

Numerade Educator

Problem 8

Two blocks of masses $m_{1}=4 \mathrm{~kg}$ and $m_{2}=2 \mathrm{~kg}$ are connected to the ends of a string which passes over a massless, frictionless pulley. The total downward thrust on the pulley is nearly
(a) $27 \mathrm{~N}$
(b) $54 \mathrm{~N}$
(c) $0.8 \mathrm{~N}$
(d) zero

Aniket Bajaj

Numerade Educator

Problem 9

A man wants to slide down a rope. The breaking load for the rope $\frac{2}{3}$ rd of the weight of the man. With what minimum acceleration should fireman slide down?
(a) $\frac{g}{4}$
(b) $\frac{g}{3}$
(c) $\frac{2 g}{3}$
(d) $\frac{g}{6}$

Dheeraj Sharma

Numerade Educator

Problem 10

A body weighs $8 \mathrm{~g}$ when placed in one pan and $18 \mathrm{~g}$. when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is.
(a) $13 \mathrm{~g}$
(b) $12 \mathrm{~g}$
(c) $15.5 \mathrm{~g}$
(d) $15 \mathrm{~g}$

Raj Bala

Numerade Educator

Problem 11

A body of mass $5 \mathrm{~kg}$ is acted upon by two perpendicular forces $8 \mathrm{~N}$ and $6 \mathrm{~N}$. Give the magnitude and direction of the acceleration of the body
(a) $2 \mathrm{~m} / \mathrm{s}^{2}$ at an angle $3 \underline{*}$ to force
(b) $2 \mathrm{~m} / \mathrm{s}^{2}$ at an angle $57^{\prime}$ to force
(c) $4 \mathrm{~m} / \mathrm{s}^{2}$ at angle $37^{*}$ to force
(d) $4 \mathrm{~m} / \mathrm{s}^{2}$ at an angle 57 to force

Dheeraj Sharma

Numerade Educator

Problem 12

A sphere is accelerated upward by a cord whose breaking strength is four times its weight. The maximum acceleration with which the sphere can move up without breaking the cord is
(a) $g$
(b) $3 \mathrm{~g}$
(c) $2 \mathrm{~g}$
(d) $4 \mathrm{~g}$

Raj Bala

Numerade Educator

Problem 13

A body of mass $2 \mathrm{~kg}$ travels according to law $x(t)=p t+q t^{2}+r t^{3}$, where $p=3 \mathrm{~ms}^{-1}, q=4 \mathrm{~ms}^{-1}$ and
$r=5 \mathrm{~ms}^{-3}$. The force acting on the body at $t=2 \mathrm{~s}$ is [NCFRT Exemplat]
(a) $136 \mathrm{~N}$
(b) $134 \mathrm{~N}$
(c) $158 \mathrm{~N}$
(d) $68 \mathrm{~N}$

Dheeraj Sharma

Numerade Educator

Problem 14

The adjacent figure is the part of a horizontally stretched net section $A B$ is stretched with a force of $10 \mathrm{~N}$. The tension in the seetion $B C$ and $B F$ are
(a) $10 \mathrm{~N}, 11 \mathrm{~N}$
(b) $10 \mathrm{~N}, 6 \mathrm{~N}$
(c) $10 \mathrm{~N}, 10 \mathrm{~N}$
(d) Can't calculate due to insufficient data

Hast Aggarwal

Numerade Educator

Problem 15

A bag of sand of mass $m$ is suspended by a rope. $A$ bullet of mass $\frac{m}{20}$ is fired at it with a velocity $v$ and gets embedded into it. The velocity of the bag finally is
(a) $\frac{v}{20} \times 21$
(b) $\frac{20 \mathrm{v}}{21}$
(c) $\frac{v}{20}$
(d) $\frac{v}{21}$

Narayan Hari

Numerade Educator

Problem 16

The engine of a car produces an acceleration of $6 \mathrm{~ms}^{-2}$ in the car. If this car pulls another car of the same mass, then the acceleration would be
(a) $6 \mathrm{~ms}^{-2}$
(b) $12 \mathrm{~ms}^{-2}$
(c) $3 \mathrm{~ms}^{-2}$
(d) $1.5 \mathrm{~ms}^{-2}$

Saman Zulfiqar

Numerade Educator

Problem 17

A constant force aeting on a body of mass $3.0 \mathrm{~kg}$ changes its speed from $2.0 \mathrm{~m} / \mathrm{s}$ to $3.5 \mathrm{~s}$. The direction of motion of the body remains unehanged. What is the magnitude and direction of the force?
(a) $0.18 \mathrm{~N}$, along the direction of motion
(b) $0.18 \mathrm{~N}$, opposite to the direction of motion
(c) $0.28 \mathrm{~N}$, along the direction of motion
(d) $0.28 \mathrm{~N}$, opposite to the direction of motion

Akshaya Rs

Numerade Educator

Problem 18

If a body of mass $m$ is moving on a rough horizontal surface of coefficient of kinetic friction $\mu$, the net electromagnetic force exerted by surface on the body 18
(a) $m g \sqrt{1+\mu^{2}}$
(b) $\mu \mathrm{mg}$
(c) $\mathrm{mg}$
(d) $m g \sqrt{1-\mu^{2}}$

Saman Zulfiqar

Numerade Educator

Problem 19

An open carriage in a goods train is moving with a uniform velocity of $10 \mathrm{~ms}^{-1}$. If the rain adds water with zero velocity at the rate of $5 \mathrm{kgs}^{-1}$, then the additional force applied by the engine to maintain the same velocity of the train is
(a) $0.5 \mathrm{~N}$
(b) $2.0 \mathrm{~N}$
(c) $50 \mathrm{~N}$
(d) $25 \mathrm{~N}$

Martina De Stefano

Martina De Stefano

Numerade Educator

Problem 20

A batsman deflects a ball by an angle of $45^{\circ}$ without changing its initial speed which equal to $54 \mathrm{~km} / \mathrm{h}$. What is the impulse imparted to the ball? (Mass of the ball is $0.15 \mathrm{~kg}$ ).
(a) $4 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$
(b) $\mathrm{kg}-\mathrm{m} / \mathrm{s}$
(c) $2 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$
(d) $5 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$

Sanu Kumar

Numerade Educator

Problem 21

A body floats in a liquid contained in a beaker. If the whole system as shown in figure of all freely under gravity, then the upthrust on the body due to liquid is
(a) zero
(b) equal to the weight of liquid displaced
(c) equal to the weight of the body in air
(d) None of the above

Baskar P

Numerade Educator

Problem 22

An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are $2 p$ i and $p \mathbf{j}$. The momentum of the third part
(a) will have a magnitude $p \sqrt{3}$
(b) will have a magnitude $p \sqrt{5}$
(c) will have a magmitude $p$
(d) will have a magnitude $2 p$

Mirza Aslam Beig

Mirza Aslam Beig

Numerade Educator

Problem 23

In figure, the blocks $A, B$ and $C$ each of mass $m$ have acceleration $a_{1}, a_{2}$ and $a_{3}$ respectively. $F_{1}$ and $F_{2}$ are external forces of magnitude $2 \mathrm{mg}$ and $\mathrm{mg}$ respectively. Then
$(a) a_{1}=a_{2}=a_{1}$
(b) $a_{1}>a_{1}>a_{2}$
(c) $a_{1}=a_{2}, a_{2}=a_{1}$
(d) $a_{1}=a_{1}, a_{1}=a_{1}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 24

If the surface is smooth, the acceleration of the block $m_{2}$ will be
(a) $\frac{m_{2} g}{4 m_{1}+m_{1}}$
(b) $\frac{2 m_{2} g}{4 m_{1}+m_{2}}$
(c) $\frac{2 m_{1} g}{m_{1}+4 m_{2}}$
(d) $\frac{2 m \cdot g}{m_{1}+m_{2}}$

Saman Zulfiqar

Numerade Educator

Problem 25

If a force of $250 \mathrm{~N}$ act on body the momentum acquired is $125 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$. What is the period for which force acts on the body?
(a) $0.5 \mathrm{~s}$
(b) $0.2 \mathrm{~s}$
(c) $0.4 \mathrm{~s}$
(d) $0.25 \mathrm{~s}$

Vysakh M

Numerade Educator

Problem 26

A point mass $m$ is moving along inclined plane with acceleration $a$ with respect to smooth triangular block. The triangular block is moving horizontally with acceleration $a_{0}$. The value of $a$ is
(a) $g \sin \theta+a_{0} \cos \theta$
(b) $g \sin \theta-a_{0} \cos \theta$
(c) $g \cos \theta-a_{0} \sin \theta$
(d) None of these

Narayan Hari

Numerade Educator

Problem 27

When a force $F$ acts on a body of mass $m$, the acceleration produced in the body is $a$. If three equal forces $F_{1}=F_{2}=F_{3}=F$ act on the same body as shown in figure, $_{5}$ the acceleration produced is
(a) $(\sqrt{2}-1) a$
(b) $(\sqrt{2}+1) a$
(c) $\sqrt{2} a$
(d) a

Sanu Kumar

Numerade Educator

Problem 28

Two weights $w_{1}$ and $w_{2}$ are suspended from the ends of a light string over a smooth fixed pulley. If the pulley is pulled up with acceleration $g$, the tension in the string will be
(a) $\frac{4 w w_{2}}{w_{1}+w_{2}}$
(b) $\frac{2 w w_{2}}{w_{1}+w_{2}}$
(c) $\frac{w_{1}-w_{2}}{w_{1}+w_{j}}$
(d) $\frac{w_{1} w_{2}}{2\left(w_{1}+w_{2}\right)}$

Dheeraj Sharma

Numerade Educator

Problem 29

A ball of mass $1 \mathrm{~kg}$ hangs in equilibrium from two strings $O A$ and $O B$ as shown in figure. What are the tensions in strings $O A$ and $O B ?$ (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $5 \mathrm{~N}$, zero
(b) Zero, $\mathrm{N}$
(c) $5 \mathrm{~N}, 5 \sqrt{3} \mathrm{~N}$
(d) $5 \sqrt{3} \mathrm{~N}, 5 \mathrm{~N}$

Raj Bala

Numerade Educator

Problem 30

A dise of mass $10 \mathrm{~g}$ is kept floating horizontally in air by firing bullets, each of mass $5 \mathrm{~g}$, with the same velocity at the same rate of 10 bullets per second. The bullets rebound with the same speed in positive direction. The velocity of each bullet at the time of impact is
(a) $196 \mathrm{cms}^{-1}$
(b) $98 \mathrm{cms}^{-1}$
(c) $49 \mathrm{cms}^{-1}$
(d) $392 \mathrm{cms}^{-1}$

Saman Zulfiqar

Numerade Educator

Problem 31

A ball is travelling with uniform translatory motion. This means that
(a) it is at rest
(b) the path can be a straight line or circular and the ball travels with uniform speed
(c) all parts of the ball have the same velocity [magnitude and direction] and the velocity is constant
(d) the centre of the ball moves with constant velocity and the ball spins about its centre unifomly

Dheeraj Sharma

Numerade Educator

Problem 32

A satellite in force free space sweeps stationary interplanetary dust at a rate $d M / d t=\alpha w$, where $M$ is the mass, $v$ is the velocity of the satellite and $\alpha$ is a constant. What is the deacceleration of the satellite?
(a) $-2 \mathrm{~cm}^{2} / \mathrm{M}$
(b) $-\alpha v^{2} / M$
$(\mathbf{c})+\alpha_{\underline{ }^{2}} / M$
(d) $-\alpha v^{2}$

Nikhil Choudhary

Nikhil Choudhary

Numerade Educator

Problem 33

A metre scale is moving with uniform velocity. This implies $\quad$ NCFRT Exemplar]
(a) the force acting on the scale is zero, but a torque about the centre of mass can act on the seale
(b) the force acting on the scale is zero and the torque acting ahout centre of mass of the scale is also zero
(c) the total force acting on it need not be zero but the torque on it is zeto
(d) neither the force nor the torque need to be zero

Dheeraj Sharma

Numerade Educator

Problem 34

A bird is sitting in a large closed cage which is placed on a spring balance. It records a weight of $25 \mathrm{~N}$. The bird (mass $m=0.5 \mathrm{~kg}$ ) flies upward in the cage with an acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$. The spring balance will now record a weight of
(a) $24 \mathrm{~N}$
(b) $25 \mathrm{~N}$
(c) $26 \mathrm{~N}$
(d) $27 \mathrm{~N}$

Raj Bala

Numerade Educator

Problem 35

A cricket ball of mass $150 \mathrm{~g}$ has an initially velocity $u=(3 \hat{\mathbf{i}}+4 \hat{j}) \mathrm{ms}^{-1}$ and a final velocity $v=(-3 \hat{i}+4 \hat{j}) \mathrm{ms}^{-1}$. After behind hit. The change in momentum (final momentum-initial momentum) is (in $\mathrm{kg} \mathrm{ms}^{-1}$ )
[NCERT|
(a) zero
(b) $-(0.45 \hat{i}+0.6 \hat{j})$
(c) $-(0.9 \hat{i}+1.2 j)$
(d) $-5(\hat{i}+i)$

Vysakh M

Numerade Educator

Problem 36

In the above question the magnitude of the momentum transferred during the hit is [NCERT]
(a) zero
(b) $0.75 \mathrm{~kg} \mathrm{~ms}^{-1}$
(c) $1.5 \mathrm{~kg} \mathrm{~ms}^{-1}$
(d) $14 \mathrm{~kg} \mathrm{~ms}^{-1}$

Ravindra Yadav

Numerade Educator

Problem 37

A frictionless inclined plane of length $l$ having inclination $\theta$ is placed inside a lift which is accelerating downward with an acceleration $a(<g)$. If a block is allowed to move, down the inclined plane, from rest, then the time taken by the block to slide from top of the inclined plane to the bottom of the inclined plane is
(a) $\sqrt{\frac{2 l}{g}}$
(b) $\sqrt{\frac{2 l}{g-a}}$
(c) $\sqrt{\frac{2 l}{g+a}}$
(d) $\sqrt{\frac{2 l}{(g-a) \sin \theta}}$

Prem Bijarniya

Numerade Educator

Problem 38

A rocket with a lift-off mass $10^{5} \mathrm{~kg}$ is blasted upward with an initial acceleration of $5 \mathrm{~ms}^{-2}$. If $g=10 \mathrm{~ms}^{-2}$, then the initial thrust of the blast is
(a) $1.5 \times 10^{2} \mathrm{~N}$
(b) $1.5 \times 10^{3} \mathrm{~N}$
(c) $1.5 \times 10^{5} \mathrm{~N}$
(d) $1.5 \times 10^{6} \mathrm{~N}$

Dheeraj Sharma

Numerade Educator

Problem 39

A block of mass $\sqrt{3} \mathrm{~kg}$ rests on a horizontal frictionless $x y$-plane. What would be the acceleration of the block if it is subjected to two forces as shown in figure?
(a) $2.5 \mathrm{~ms}^{-2}$
(b) $5 \mathrm{~ms}^{-2}$ along $y$-axis
(c) $10 \mathrm{~ms}^{-2}$ along $x$-axis
(d) $15 \mathrm{~ms}^{-2}$ along $y$-axis

Yuva S

Numerade Educator

Problem 40

Two masses of $3 \mathrm{~kg}$ and $5 \mathrm{~kg}$ are suspended from the ends of an unstreatchable massless cord passing over a frictionless pulley. When the masses are released, the pressure on the pulley is
(a) $2 \mathrm{~kg} \mathrm{f}$
(b) $7.5 \mathrm{~kg}$ f
(c) $8 \mathrm{~kg} \mathrm{f}$
(d) $15 \mathrm{kgf}$

Raj Bala

Numerade Educator

Problem 41

In a rocket of mass $1000 \mathrm{~kg}$ fuel is consumed at a rate of $40 \mathrm{~kg} / \mathrm{s}$. The velocity of the gases ejected from the rocket is $5 \times 10^{4} \mathrm{~m} / \mathrm{s}$. The thrust on the rocket is
(a) $2 \times 10^{3} \mathrm{~N}$
(b) $5 \times 10^{4} \mathrm{~N}$
(c) $2 \times 10^{6} \mathrm{~N}$
(d) $2 \times 10^{9} \mathrm{~N}$

Raj Bala

Numerade Educator

Problem 42

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) $g \operatorname{cosec} \alpha$

Dheeraj Sharma

Numerade Educator

Problem 43

A horizontal force $F$ is applied on a block of mass $m$ placed on
a rough inclined plane of inclination
6. The normal reaction $N$ is
(a) $m g \cos \theta$
(b) $m g \sin \theta$
(c) $m g \cos \theta-F \cos \theta$
(d) $m g \cos \theta+F \sin \theta$

Ajay Singhal

Numerade Educator

Problem 44

For the system shown in figure, the pulleys are light and frictionless. The tension in the string will be
(a) $2 \mathrm{mg} \sin \theta$
(b) $\frac{3}{2} m g \sin$
(c) $\frac{1}{2} m g \sin \theta$
(d) $2 \mathrm{mg} \sin \theta$

Saman Zulfiqar

Numerade Educator

Problem 45

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) $g\left(l^{2}-1\right)$
(c) $\frac{g}{\sqrt{p^{2}}}$
(d) $\frac{g}{l^{2}-1}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 46

1. The monkey $B$ shown in figure is holding on to the tail of the monkey $A$ which is climbing up a rope. The masses of the monkeys $A$ and $B$ are $5 \mathrm{~kg}$ and $2 \mathrm{~kg}$ respectively. If $A$ can tolerate a tension of $30 \mathrm{~N}$ in its tail, what force should it apply on the rope in order to carry the monkey $B$, $B$ with it? (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $105 \mathrm{~N}$
(b) $108 \mathrm{~N}$
(c) $10.5 \mathrm{~N}$
(d) $100 \mathrm{~N}$

Vipender Rao

Numerade Educator

Problem 48

The acceleration of the 500 g block in figure is
(a) $\frac{6 g}{13}$ downwards
(b) $\frac{7 g}{13}$ downwards
(c) $\frac{8 g}{13}$ downwards
(d) $\frac{9 g}{12}$ upwards

Prabhu Ramji

Numerade Educator

Problem 49

A body with mass $5 \mathrm{~kg}$ is acted upon by a force $\mathbf{F}=(-3 \hat{\mathbf{i}}+4 \hat{j}) \mathrm{N}$. If its initial velocity at $t=0$ is $\mathbf{v}=(6 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}) \mathrm{ms}^{-1}$, the time at which it will just have
a velocity along the $y$-axis is
(a) never
(b) $10 \mathrm{~s}$
(c) $2 \mathrm{~s}$
(d) $15 \mathrm{~s}$

Dheeraj Sharma

Numerade Educator

Problem 50

A $1000 \mathrm{~kg}$ lift is supported by a cable that can support $2000 \mathrm{~kg}$. The shortest distance in which the lift can be stopped when it is descending with a speed of $2.5 \mathrm{~ms}^{-1}$ is [Take $\left.g=10 \mathrm{~ms}^{-2}\right]$
(a) $1 \mathrm{~m}$
(b) $2 \mathrm{~m}$
(c) $\frac{5}{32} \mathrm{~m}$
(d) $\frac{5}{16} \mathrm{~m}$

Ajay Singhal

Numerade Educator

Problem 51

A block of weight $5 \mathrm{~N}$ is pushed against a vertical wall by a force $12 \mathrm{~N}$. The coefficient of friction between the wall and block is $0.6$. The magnitude of the force exerted by the wall on the block is
(a) $12 \mathrm{~N}$
(b) $5 \mathrm{~N}$
(c) $7.2 \mathrm{~N}$
(d) $13 \mathrm{~N}$

Averell Hause

Carnegie Mellon University

Problem 52

A blumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination $30^{\circ}$ with horizontal. Acceleration of train up the plane is $a=9 / 2$. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is
(a) $30^{\circ}$
(b) $\tan ^{-1}\left(\frac{2}{\sqrt{3}}\right)$ (c) $\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
(d) $\tan ^{-1}(2)$

Narayan Hari

Numerade Educator

Problem 53

A block is gently placed on a conveyor belt moving horizontally with constant speed. After 4 s the velocity of the block becomes equal to the velocity of belt. If the coefficient of friction between the block and the belt is 0.2, then velocity of the conveyor belt is
(a) $2 \mathrm{~ms}^{-1}$
(b) $4 \mathrm{~ms}^{-1}$
(c) $6 \mathrm{~ms}^{-1}$
(d) $8 \mathrm{~ms}^{-1}$

Ajay Singhal

Numerade Educator

Problem 54

A cricket ball of mass 150 g collides straight with a bat with a velocity of $10 \mathrm{~ms}^{-1}$. Batsman hits it straight back with a velocity of $20 \mathrm{~ms}^{-1}$, If ball remains in contact with bat for $0.18$, then average force exerted by the bat on the ball is
(a) $15 \mathrm{~N}$
(b) $45 \mathrm{~N}$
(c) $150 \mathrm{~N}$
(d) $4.5 \mathrm{~N}$

Ajay Singhal

Numerade Educator

Problem 55

A block of mass $1 \mathrm{~kg}$ is at rest on a horizontal table. The coefficient of static friction between the block and the table is $0.5$. If $g=10 \mathrm{~ms}^{-2}$, then the magnitude of the force acting upwards at an angle of $60^{\circ}$ from the horizontal that will just start the block moving is
(a) $5 \mathrm{~N}$
(b) $5.36 \mathrm{~N}$
(c) $74.6 \mathrm{~N}$
(d) $10 \mathrm{~N}$

Ajay Singhal

Numerade Educator

Problem 56

$100 \mathrm{~g}$ of an iron ball having velocity $10 \mathrm{~ms}^{-1}$ collides with wall at an angle $30^{\circ}$ and rebounds with the same angle. If the period of contact between the ball and wall is $0.1 \mathrm{~s}$, then the average force experienced by the wall is
(a) $10 \mathrm{~N}$
(b) $100 \mathrm{~N}$
(c) $1.0 \mathrm{~N}$
(d) $0.1 \mathrm{~N}$

Narayan Hari

Numerade Educator

Problem 57

A heavy uniform chain lies on a horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$ then the maximum fraction of length of the chain, that can hang over one edge of the table is
(a) $20 \%$
(b) $25 \%$
(c) $35 \%$
(d) 1576

Narayan Hari

Numerade Educator

Problem 58

A block $A$ with mass $100 \mathrm{~kg}$ is resting on another block $B$ of mass $200 \mathrm{~kg}$. As shown in figure, a horizontal rope tied to a wall holds it. The coefficient of friction between $A$ and $B$ is $0.2$ while coefficient of friction between $B$ and the ground is 0.3. The minimum required force $F$ to start moving $B$ will be
(a) $900 \mathrm{~N}$
(b) $100 \mathrm{~N}$
(c) $1100 \mathrm{~N}$
(d) $1200 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 59

A 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) $\mu \mathrm{Rg}$
(b) $R g \sqrt{\mu}$
(c) $\mu \sqrt{R g}$
(d) $\sqrt{\mu \mathbb{R g}}$

Ajay Singhal

Numerade Educator

Problem 60

A chain lies on a rough horizontal table. It starts sliding when one-fourth of its length hangs over the edge of the table. The coefficient of static friction between the chain and the surface of the table is
(a) $\frac{1}{2}$
(b) $\frac{1}{3}$
(c) $\frac{1}{4}$
(d) $\frac{1}{5}$

Ravindra Yadav

Numerade Educator

Problem 61

A fireman of mass $60 \mathrm{~kg}$ slides down a pole He is pressing the pole with a force of $600 \mathrm{~N}$. The coefficient of friction between the hands and the pole is $0.5$ with what acceleration with the fireman slide down? $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $1 \mathrm{~m} / \mathrm{s}^{2}$
(b) $2.5 \mathrm{~m} / \mathrm{s}^{2}$
(c) $10 \mathrm{~m} / \mathrm{s}^{2}$
(d) $5 \mathrm{~m} / \mathrm{s}^{2}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 62

The minimum velocity (in $\mathrm{ms}^{-1}$ ) with which a car driver must traverse a flat curve of radius $150 \mathrm{~m}$ and coefficient of friction $0.6$ to avoid skidding is
(a) $60 \mathrm{~ms}^{-1}$
(b) $30 \mathrm{~ms}^{-1}$
(c) $15 \mathrm{~ms}^{-1}$
(d) $25 \mathrm{~ms}^{-1}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 63

A block of mass $\sqrt{3} \mathrm{~kg}$ resting on a horizontal surface. A force $F$ is applied on the block as shown in figure. If coefficient of friction between the block be $\frac{1}{2 \sqrt{3}}$ what can be the maximum value of force $F$ so that block does not start moving? (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $20 \mathrm{~N}$
(b) $10 \mathrm{~N}$
(c) $12 \mathrm{~N}$
(d) $15 \mathrm{~N}$

Charles Machakwa

Charles Machakwa

Numerade Educator

Problem 64

A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$, then the maximum fraction of the length of the chain that can hang over one edge of the table is
(a) $20 \%$
(b) $25 \%_{6}$
(c) $35 \%$
(d) $15^{\circ 6}$

Narayan Hari

Numerade Educator

Problem 65

A block moves down a smooth inclined plane of inclination 0 . Its velocity on reaching the bottom is $v$. If it slides down a rough inclined plane of same inelination, its velocity on reaching the bottom is $w / n$, where $n$ is a number greater than 1 . The coefficient of friction is given by
(a) $\mu=\tan \theta\left(1-\frac{1}{n^{2}}\right)$
(b) $\mu=\cot \theta\left(1-\frac{1}{n^{2}}\right)$
(c) $\mu=\tan \theta\left(1-\frac{1}{n^{2}}\right)^{1 / 2}$
(d) $\mu=\cot \theta\left(1-\frac{1}{n^{2}}\right)^{1 / 2}$

Nishant Kumar

Numerade Educator

Problem 66

A smooth inclined plane of length $L$ having inclination $\theta$ with the horizontal is inside a lift which is moving down with retardation $a$. The time taken by a body to slide down the inclined plane, from rest, will be
(a) $\sqrt{\frac{2 L}{(g+a) \sin \theta}}$
(b) $\sqrt{\frac{2 L}{(g-a) \sin \theta}}$
(c) $\sqrt{\frac{2 L}{g \sin \theta}}$
(d) $\sqrt{\frac{2 L}{a \sin \theta}}$

RZ

Rubeena Zulfiqar

Numerade Educator

Problem 67

A wooden box of mass $8 \mathrm{~kg}$ slides down an inclined plane of inclination $30^{\circ}$ to the horizontal with a constant acceleration of $0.4 \mathrm{~ms}^{-2}$. What is the force of friction between the box and inclined plane? $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $36.8 \mathrm{~N}$
(b) $76.8 \mathrm{~N}$
(c) $65.6 \mathrm{~N}$
(d) $97.8 \mathrm{~N}$

Salamat Ali

Numerade Educator

Problem 68

The coefficient of kinetic friction between a $20 \mathrm{~kg}$ box and the floor is $0.40$. How much work does a pulling force do on the box in pulling it $8.0 \mathrm{~m}$ across the floor at constant speed? The pulling force is directed $37^{\circ}$ above the horizontal
(a) $343 \mathrm{~J}$
(b) $482 \mathrm{~J}$
(c) $14.4 \mathrm{~J}$
(d) None of these

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 69

A car starts from rest to cover a distance s. The coefficient of friction between the road and the tyres is $m$. The minimum time in which the car can cover the distance is proportional to
(a) $\mu$
(b) $\sqrt{\mu}$
(c) $1 / \mathrm{\mu}$
(d) $1 / \sqrt{\mu}$

Nishant Kumar

Numerade Educator

Problem 70

A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta$ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is
(a) $\frac{P+Q \sin \theta}{m g+O \cos \theta}$
(b) $\frac{P \cos \theta+Q}{m g-0 \sin \theta}$
(c) $\frac{P+Q \cos \theta}{m g+Q \sin \theta}$
(d) $\frac{P \sin \theta-Q}{m g-O \cos \theta}$

Dheeraj Sharma

Numerade Educator

Problem 71

A partly hanging uniform chain of length $L$ is resting on a rough horizontal table. $l$ is the maximum possible length that can hang in equilibrium. The coefficient of friction between the chain and table is
(a) $\frac{1}{L-1}$
(b) $\frac{L}{l}$
(c) $\frac{l}{L}$
(d) $\frac{A}{L+l}$

Narayan Hari

Numerade Educator

Problem 72

A box of mass $m \mathrm{~kg}$ is placed on the rear side of an open truck accelerating at $4 \mathrm{~ms}^{-2}$. The coefficient of friction between the box and the surface below it is 0.4. The net acceleration of the box with respect to the truck is zero. The value of $m$ is $\left[\right.$ Given $\left.g=10 \mathrm{~ms}^{-2}\right]$
(a) $4 \mathrm{~kg}$
(b) $8 \mathrm{~kg}$
(c) $9.78 \mathrm{~kg}$
(d) It could be any value

Dheeraj Sharma

Numerade Educator

Problem 73

A $40 \mathrm{~kg}$ slab rests on a frictionless floor. A $10 \mathrm{~kg}$ block rests on top of the slab. The static coefficient of friction between the block and the slab is $0.60$ while the kinetic coefficient of friction is $0.40$. The $10 \mathrm{~kg}$ block is acted upon by a horizontal force of $100 \mathrm{~N}$. If $g=9.8 \mathrm{~ms}^{-2}$, the resulting acceleration of the slab will be
(a) $1.47 \mathrm{~ms}^{-2}$
(b) $1.69 \mathrm{~ms}^{-2}$
(c) $9.8 \mathrm{~ms}^{-2}$
(d) $0.98 \mathrm{~ms}^{-2}$

Stephen Zaffke

Numerade Educator

Problem 74

A body of mass $40 \mathrm{~kg}$ resting on a rough horizontal surface is subjected to a force $P$ which is just enough to start the motion of the body. If $\mu_{n}=0.5, \mu_{k}=0.4$, $g=10 \mathrm{~ms}^{-2}$ and the force $P$ is continuously applied on the body, then the acceleration of the body is
(a) $2 \mathrm{rro}$
(b) $1 \mathrm{~ms}^{-2}$
(c) $2 \mathrm{~ms}^{-2}$
(d) $2.4 \mathrm{~ms}^{-2}$

Ajay Singhal

Numerade Educator

Problem 75

The coefficient of friction between a body and the surface of an inclined plane at $45^{\circ}$ is $0.5$ if $g=9.8 \mathrm{~m} / \mathrm{s}^{2} .$ The acceleration of the body downwards in $\mathrm{m} / \mathrm{s}^{2}$ is
(a) $\frac{4.9}{\sqrt{2}}$
(b) $4.9 \sqrt{2}$
(c) $19.2 \sqrt{2}$
(d) $4.9$

Ajay Singhal

Numerade Educator

Problem 76

A rope of length $L$ and mass $M$ is hanging from a right support. The tension in the rope at a distance $x$ from the rigid support is
(a) $\mathrm{Mg}$
(b) $\left(\frac{L-x}{L}\right) M g$
(c) $\left(\frac{L}{L-x}\right) \mathrm{Mg}$
(d) $\frac{x}{L} M g$

Ajay Singhal

Numerade Educator

Problem 77

A plate of mass $M$ is placed on a horizontal frictionless surface (see figure) and a body of mass $m$ is placed on this plate. The coefficient of dynamics friction between this body and the plate is $\mu$. If a force $2 \mu m g$ is applied to the body of mass $m$ along the horizontal, the acceleration of the plate will be
(a) $\frac{\mu m}{M} g$
(b) $\frac{\mu m}{(M+m)} g$
(c) $\frac{2 \mu m}{M} g$
(d) $\frac{2 \mu m}{(M+m)} g$

Narayan Hari

Numerade Educator

Problem 78

A man weighing $60 \mathrm{~kg}$ is standing on a trolley weighing $240 \mathrm{~kg}$. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a velocity of $1 \mathrm{~ms}^{-1}$, then after $4 \mathrm{~s}$, his displacement relative to the ground is
(a) $6 \mathrm{~m}$
(b) $4.8 \mathrm{~m}$
(c) $3.2 \mathrm{~m}$
(d) $2.4 \mathrm{~m}$

Nishant Kumar

Numerade Educator

Problem 79

A block of mass $5 \mathrm{~kg}$, resting on a horizontal surface, is connected by a cord, passing over a light frictionless pulley to a hanging block of mass $5 \mathrm{~kg}$. The coefficient of kinetic friction between the block and the surface is $0.5$. Tension in the cord is (Take $g=$ $9.8 \mathrm{~ms}^{-2}$ )
(a) $49 \mathrm{~N}$
(b) $36 \mathrm{~N}$
(c) $36.75 \mathrm{~N}$
(d) $2.45 \mathrm{~N}$

Ajay Singhal

Numerade Educator

Problem 80

Three blocks are placed at rest on a smooth inclined plane with force acting on $m_{1}$ parallel to the inclined plane. Find the contact force between $m_{2}$ and $m_{3}$ -
(a) $\frac{\left(m_{1}+m_{2}+m_{1}\right) F}{m_{1}}$
(b) $\frac{m_{1} F}{m_{1}+m_{1}+m_{1}}$
(c) $F-\left(m_{1}+m_{1}\right) g$
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 81

Three equal weight $A, B$ and $C$ of mass $2 \mathrm{~kg}$ each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weight $B$ and $C$ is
(a) zero
(b) $13 \mathrm{~N}$
(c) $3.3 \mathrm{~N}$
(d) $19.6 \mathrm{~N}$

Ajay Singhal

Numerade Educator

Problem 82

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force applied on the upper string produces an acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$ in the upward direction in both the blocks. If $T$ and $T^{\prime}$ be the tensions in the two parts of the string, then $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $T=70.8 \mathrm{~N}$ and $T^{\prime}=47,2 \mathrm{~N}$
(b) $T=58.8 \mathrm{~N}$ and $T^{*}=47.2 \mathrm{~N}$
(c) $T=70.8 \mathrm{~N}$ and $T^{\prime}=58.8 \mathrm{~N}$
(d) $T=70.8 \mathrm{~N}$ and $T^{\prime}=0$

Raj Bala

Numerade Educator

Problem 83

A block is dragged on a smooth horizontal plane with the help of a light rope which moves with a velocity as shown in figure. The horizontal velocity of the block is
(a) $v$
(b) $v \sin \theta$
(c) $\frac{v}{\sin \theta}$
(d) $\frac{v}{\cos \theta}$

Dheeraj Sharma

Numerade Educator

Problem 84

A mass of $3 \mathrm{~kg}$ descending vertically downward supports a mass of $2 \mathrm{~kg}$ by means the end of $5 \mathrm{~s}$, the string breaks. How much higher the $2 \mathrm{~kg}$ mass will go further?
(a) $4.9 \mathrm{~m}$
(b) $9.8 \mathrm{~m}$
(c) $19.6 \mathrm{~m}$
(d) $2.45 \mathrm{~m}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 85

Two bodies of masses $m_{1}$ and $m_{2}$ are connected by a light, inextensible string which passes over a frictionless pulley. If the pulley is moving upward with uniform acceleration $g$, then the tension in the string is
(a) $\frac{4 m m_{2}}{m_{1}+m_{1}} g$
(b) $\frac{m_{1} m_{2}}{4 m_{1} m_{2}} g$
(c) $\frac{m_{1} m_{2}}{m_{1}+m_{1}} g$
(d) $\frac{m_{1}-m_{1}}{m_{1}+m_{1}} g^{2}$

Ajay Singhal

Numerade Educator

Problem 86

In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to nth mass is
(a) $\frac{\mathrm{mHlg}}{n m+M}$
(b) $\frac{m M g}{n m M}$
(c) $m g$
(d) mhg

Nishant Kumar

Numerade Educator

Problem 87

In the figure, the ball $A$ is released from rest when the spring is at its natural length. For the block $B$ of mass $M$ to leave contact with the ground at same stage, the minimum mass of $A$ must be
(a) $2 \mathrm{M}$
(b) $\bar{M}$
(c) $\frac{M}{2}$
(d) a function of $\bar{M}$ and the force constant of the spring

Narayan Hari

Numerade Educator

Problem 88

A shell is fired from a cannon with velocity $v \mathrm{~ms}^{-1}$ at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass, One of the pieces retraces its path to the cannon and the speed in $\mathrm{m} / \mathrm{s}$ of the piece immediately after the explosion is
(a) $3 v \cos \theta$
(b) $2 v \cos \theta$
(c) $\frac{3 \mathrm{~V}}{2} \cos \theta$
(d) $\frac{\sqrt{3} v \cos \theta}{2}$

Hast Aggarwal

Numerade Educator

Problem 89

2
$A$ body of weight $2 \mathrm{~kg}$ is suspended as shown in figure. The tension $T_{1}$ in the horizontal string (in $\mathrm{kg}-\mathrm{wt}$ ) is
$(a) 2 / \sqrt{3}$
(b) $\sqrt{3} / 2$
(c) $2 \sqrt{3}$
(d) 2

Dheeraj Sharma

Numerade Educator

Problem 90

Two blocks of masses $m$ and $2 m$ 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 $2 \mathrm{~m}$ hangs vertically. If the system is released, the blocks move with an acceleration equal to
(a) $\frac{g}{4}$
(b) $\frac{g}{3}$
(c) $\frac{g}{2}$
(d) $g$

Vysakh M

Numerade Educator

Problem 91

Refer to the system shown in figure. The ratio of tensions $T_{1}$ and $T_{2}$ is
(a) $\frac{m_{1}}{m_{1}+m_{2}}$
(b) $\frac{m_{2}}{m_{1}+m_{2}}$
(c) $\frac{m_{1}}{m_{2}}$
(d) $\frac{m_{2}}{m_{1}}$

Narayan Hari

Numerade Educator

Problem 92

In the figure a smooth pulley of negligible weight is suspended by a spring balance. Weights of $1 \mathrm{~kg}$ and $5 \mathrm{~kg}$ are attached to the opposite ends of a string passing over the pulley and move with acceleration because of gravity. During their motion, the spring balance reads a weight of
[a) $6 \mathrm{~kg}$
(b) less than $6 \mathrm{~kg}$
(c) more than $6 \mathrm{~kg}$
(d) may be more or less than $6 \mathrm{~kg}$

Prabhu Ramji

Numerade Educator

Problem 93

Three blocks of masses $m_{1}, m_{2}$ and $m_{3}$ are connected 96 by massless strings as shown on a frictionless table in figure. They are pulled with a force $T_{3}=40 \mathrm{~N}$. If $m_{1}=10 \mathrm{~kg}, m_{2}=6 \mathrm{~kg}$ and $m_{\mathrm{a}}=4 \mathrm{~kg}_{1}$, the tension $T_{2}$
will be
(a) $20 \mathrm{~N}$
(b) $40 \mathrm{~N}$
(c) $10 \mathrm{~N}$
(d) $32 \mathrm{~N}$

Vysakh M

Numerade Educator

Problem 94

Refer to the system shown in figure. The acceleration of the masses is
c(a) $\frac{g}{3}$
(b) $\frac{g}{6}$
(c) $\frac{g}{9}$
(d) $\frac{g}{12}$

Aniket Bajaj

Numerade Educator

Problem 95

Two block of masses $7 \mathrm{~kg}$ and $5 \mathrm{~kg}$ are placed in contact with each other on a smooth surface. If a force of $6 \mathrm{~N}$ is applied on a heavier mass the force on the lighter mass is
(a) $3.5 \mathrm{~N}$
(b) $2.5 \mathrm{~N}$
(c) $7 \mathrm{~N}$
(d) $5 \mathrm{~N}$

Raj Bala

Numerade Educator

Problem 96

A trolley $T$ (mass $5 \mathrm{~kg}$ ) on a horizontal smooth surface is pulled by a load $L(2 \mathrm{~kg})$ through a uniform rope $A B C$ of length $2 \mathrm{~m}$ and mass $1 \mathrm{~kg} .$ As the load falls from $B C=0$ to $B C=2 \mathrm{~m}$, its acceleration (in $\mathrm{ms}^{-2}$ ) changes from (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $20 / 6$ to $20 / 5$
(b) $20 / 8$ to $30 / 8$
(c) $20 / 5$ to $30 / 6$
(d) None of these

Surendra Kumar

Numerade Educator