A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar

Chapter 4

Work, Energy, and Power - all with Video Answers

Educators

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Chapter Questions

Problem 1

The displacement-time graph of particle is shown in Fig. $4.17 .$
(A) Work done by all the forces in part $O A$ is greater than zero
(B) Work done by all the forces in part $A B$ is greater than zero
(C) Work done by all the forces in part $B C$ is greater than zero
(D) Work done by all the forces in part $A B$ is less than zero

Mahendra K

Mahendra K

Numerade Educator

Problem 2

A small block of mass $0.1 \mathrm{~kg}$ is pressed against a horizontal spring fixed at one end to compress the spring through $5.0 \mathrm{~cm}$ as shown in Fig. $4.18$. The spring constant is $100 \mathrm{~N} / \mathrm{m}$. When released the block moves horizontally till it leaves the spring, it will hit the ground $2 \mathrm{~m}$ below the spring.
(A) At a horizontal distance of $1 \mathrm{~m}$ from free end of the spring.
(B) At a horizontal distance of $2 \mathrm{~m}$ from free end of the spring.
(C) Vertically below the edge on which the mass is resting.
(D) At a horizontal distance of $\sqrt{2} \mathrm{~m}$ from free end of the spring.

Dheeraj Sharma

Numerade Educator

Problem 3

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that
(A) Its velocity is constant.
(B) Its acceleration is constant.
(C) Its kinetic energy is constant.
(D) It moves in a straight line.

Dheeraj Sharma

Numerade Educator

Problem 4

Two identical balls are projected, one vertically up and the other at an angle of $30^{\circ}$ with the horizontal, with
same initial speed. The potential energy at the highest point is in the ratio
(A) $4: 3$
(B) $3: 4$
(C) $4: 1$
(D) $1: 4$

Dheeraj Sharma

Numerade Educator

Problem 5

The unit of power is
(A) Kilowatt
(B) Kilowatt-hour
(C) Dyne
(D) Joule

Dheeraj Sharma

Numerade Educator

Problem 6

A particle projected with an initial velocity $u$ at angle $\theta$ from the ground. The work done by gravity during the time it reaches the highest point $P$ is:
(A) $\frac{-m u^{2} \sin ^{2} \theta}{2}$
(B) $+\frac{m u^{2} \sin ^{2} \theta}{2}$
(C) 0
(D) $+m u^{2} \sin \theta$

Dheeraj Sharma

Numerade Educator

Problem 7

A block of mass $m$ is slowly pulled up on inclined plane of height $h$ and inclination $\theta$ with the top of a string parallel to the incline. Which of the following statement is correct for the block when it moves up from the bottom to the top of the incline?
(A) Work done by the normal reaction force is zero.
(B) Work done by the string on block is $m g h$.
(C) Work done by the gravity is $m g h$.
(D) Work done by the block is $-m g h / 2$.

Dheeraj Sharma

Numerade Educator

Problem 8

A block of mass $2 \mathrm{~kg}$ is lifted through a chain. When block moves through $2 \mathrm{~m}$ vertically the velocity becomes $4 \mathrm{~m} / \mathrm{s}$. Work done by chain force until it moves $2 \mathrm{~m}$ is $\left(g=10 \mathrm{~ms}^{-2}\right)$
(A) $40 \mathrm{~J}$
(B) $24 \mathrm{~J}$
(C) $56 \mathrm{~J}$
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 9

A position-dependent force $F=7-2 x+3 x^{2} N$ acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m} .$ The work done in joule is
(A) $70 \mathrm{~J}$
(B) $270 \mathrm{~J}$
(C) $35 \mathrm{~J}$
(D) $135 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 10

A car comes to a skidding stop in $15 \mathrm{~m}$. The force on the car due to the road is $1000 \mathrm{~N}$. The work done by road on the car and car on the road, respectively, is
(A) $-15 \mathrm{~kJ}$, zero
(B) zero, $15 \mathrm{~kJ}$
(C) $15 \mathrm{~kJ}$, zero
(D) $-15 \mathrm{~kJ}, 15 \mathrm{~kJ}$

Dheeraj Sharma

Numerade Educator

Problem 11

A particle is released from rest at origin. It moves under the influence of potential field $U=x^{2}-3 x$, where $U$ is in Joule and $x$ is in metre. Kinetic energy at $x=2 \mathrm{~m}$ will be
(A) $2 \mathrm{~J}$
(B) $1 \mathrm{~J}$
(C) $1.5 \mathrm{~J}$
(D) $0 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 12

The potential energy of a particle of mass $m$ is given by $U=\frac{1}{2} k x^{2}$ for $x<0$ and $U=0$ for $x \geq 0 .$ If total mechanical energy of the particle is $E$. Then its speed at $x=\sqrt{\frac{2 E}{k}}$ is
(A) Zero
(B) $\sqrt{\frac{2 E}{m}}$
(C) $\sqrt{\frac{E}{m}}$
(D) $\sqrt{\frac{E}{2 m}}$

Dheeraj Sharma

Numerade Educator

Problem 13

A cricket ball is hit for a six leaving the bat at an angle of $45^{\circ}$ to the horizontal with kinetic energy $K$. At the top position, the kinetic energy of the ball is
(A) Zero
(B) $K$
(C) $K / 2$
(D) $K / \sqrt{2}$

Dheeraj Sharma

Numerade Educator

Problem 14

A bullet losses $19 \%$ of its kinetic energy when passes through an obstacle. The percentage change in its speed is
(A) Reduced by $10 \%$
(B) Reduced by $19 \%$
(C) Reduced by $9.5 \%$
(D) Reduced by $11 \%$

Dheeraj Sharma

Numerade Educator

Problem 15

Two springs $A$ and $B\left(k_{A}=2 k_{B}\right)$ are stretched by applying forces of equal magnitudes at the ends. If the energy stored in $A$ is $E$, then energy stored in $B$ is
(A) $\frac{E}{2}$
(B) $2 E$
(C) $E$
(D) $\frac{E}{4}$

Dheeraj Sharma

Numerade Educator

Problem 16

A body constrained to move in $y$-direction is subjected to a force given by $\vec{F}=(-2 \vec{i}+15 \vec{j}+6 \vec{k}) N$. The work done by this force in moving the body a distance of $10 \mathrm{~m}$ along the $y$-axis is
(A) $20 \mathrm{~J}$
(B) $150 \mathrm{~J}$
(C) $60 \mathrm{~J}$
(D) $190 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 17

A particle of mass $2 \mathrm{~kg}$ starts moving in a straight line with an initial velocity of $2 \mathrm{~m} / \mathrm{s}$ at a constant acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$. The rate of change of kinetic energy is
(A) Four times the velocity at any moment.
(B) Two times the displacement at any moment.
(C) Four times the rate of change of velocity at any moment.
(D) Constant throughout.

Dheeraj Sharma

Numerade Educator

Problem 18

A block of mass $m=0.1 \mathrm{~kg}$ is released from a height of $4 \mathrm{~m}$ on a curved smooth surface. On the horizontal smooth surface, it collides with a spring of force constant $800 \mathrm{~N} / \mathrm{m}$. The maximum compression in spring will be $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $1 \mathrm{~cm}$
(B) $5 \mathrm{~cm}$
(C) $10 \mathrm{~cm}$
(D) $20 \mathrm{~cm}$

Dheeraj Sharma

Numerade Educator

Problem 19

With what minimum speed $v$ must a small ball should be pushed inside a smooth vertical tube from a height $h$ so that it may reach the top of the tube? Radius of the tube is $R$. (Assume radius of cross-section of tube is negligible in comparison to $R$.)
(A) $\sqrt{2 g(h+2 R)}$
(B) $\frac{5}{2} R$
(C) $\sqrt{g(5 R-2 h)}$
(D) $\sqrt{2 g(2 R-h)}$

Dheeraj Sharma

Numerade Educator

Problem 20

A block of mass $m=0.1 \mathrm{~kg}$ is released from a height of $4 \mathrm{~m}$ on a curved smooth surface. On the horizontal surface, path $A B$ is smooth and path $B C$ offers coefficient of friction $\mu=0.1$. If the impact of block with the vertical wall at $C$ be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be: (take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(A) $29 \mathrm{~m}$
(B) $49 \mathrm{~m}$
(C) $59 \mathrm{~m}$
(D) $109 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 21

An ideal spring with spring-constant $k$ is hung from the ceiling and a block of mass $m$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is
(A) $\frac{4 m g}{k}$
(B) $\frac{2 m g}{k}$
(C) $\frac{m g}{k}$
(D) $\frac{m g}{2 k}$

Dheeraj Sharma

Numerade Educator

Problem 22

A variable force $F$ starts acting on a block of mass $5 \mathrm{~kg}$ resting on a smooth horizontal surface. $F$ is varying with displacement $x$ as shown in $F-x$ curve. The velocity of body when its displacement is $3 \mathrm{~m}$ will be
(A) $2 \mathrm{~ms}^{-1}$
(B) $2 \sqrt{2} \mathrm{~ms}^{-1}$
(C) $2 \sqrt{3} \mathrm{~ms}^{-1}$
(D) $6 \mathrm{~ms}^{-1}$

Dheeraj Sharma

Numerade Educator

Problem 23

When a body moves in a circle, the work done by the centripetal force is always
$(\mathrm{A})>0$
(B) $<0$
(C) Zero
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 24

A force acts on a 3 gram particle such that its position $x=3 t-4 t^{2}+t^{3}$, where $x$ is in metre and $t$ is in second. The work done during first $4 \mathrm{~s}$ is
(A) $825 \mathrm{~mJ}$
(B) $285 \mathrm{~mJ}$
(C) $528 \mathrm{~mJ}$
(D) Zero

Dheeraj Sharma

Numerade Educator

Problem 25

A particle is acted upon by a conservative force $F=(7 \hat{i}-6 \hat{j}) \mathrm{N}$. The work done by the force when the particle moves from origin $(0,0)$ to the position $(-3 \mathrm{~m}$, $4 \mathrm{~m}$ ) is given by
(A) $3 \mathrm{~J}$
(B) $10 \mathrm{~J}$
(C) $-45 \mathrm{~J}$
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 26

An object of mass $10 \mathrm{~kg}$ falls from rest through a vertical distance of $10 \mathrm{~m}$ and acquires a velocity of $10 \mathrm{~m} / \mathrm{s}$. The work done by the push of air on the object is $(g=$ $\left.10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $500 \mathrm{~J}$
(B) $-500 \mathrm{~J}$
(C) $250 \mathrm{~J}$
(D) $-250 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 27

The relationship between force and position is shown in Fig. $4.19$ (in one-dimensional case). The work done by the force in displacing a body from $x=1 \mathrm{~cm}$ to $x=$ $5 \mathrm{~cm}$ is
(A) 20 ergs
(B) $60 \mathrm{ergs}$
(C) 70 ergs
(D) 700 ergs

Dheeraj Sharma

Numerade Educator

Problem 28

A particle is acted upon by a force $F=k x,(k>0)$, where $x$ is displacement of particle. If potential energy at origin is zero, then the potential energy of the particle varies with $x$ as

Dheeraj Sharma

Numerade Educator

Problem 29

A position-dependent force $F=x^{2}-3$ Newton acts on a small body of mass $2 \mathrm{~kg}$ and displaces it from $x=0$ to $x=5 \mathrm{~m}$. The work done is
(A) $110 \mathrm{~J}$
(B) $\frac{80}{3} \mathrm{~J}$
(D) $\frac{95}{2} \mathrm{~J}$
(D) Zero

Dheeraj Sharma

Numerade Educator

Problem 30

A block of mass $3 \mathrm{~kg}$ slides down a rough curved path from point $A$ as shown. If it stops at $C$, the work done by friction is $\left(g=10 \mathrm{~ms}^{-2}\right)$
(A) $-360 \mathrm{~J}$
(B) $-240 \mathrm{~J}$
(C) $-600 \mathrm{~J}$
(D) $-450 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 31

A block of mass $m$ is placed on an another rough block of mass $M$ and both are moving horizontally with same acceleration $a$ due to a force which is applied on the lower block, then work done by lower block on the upper block in moving a distance $s$ will be
(A) Mas
(B) $(m+M) a s$
(C) $\frac{M^{2}}{m} a s$
(D) $m{\text { mas }}$

Dheeraj Sharma

Numerade Educator

Problem 32

A $1 \mathrm{~kg}$ block moves towards a light spring with a velocity of $8 \mathrm{~m} / \mathrm{s}$. When the spring is compressed by $3 \mathrm{~m}$, its momentum becomes half of the original momentum. Spring constant of the spring is
(A) $18 / 3 \mathrm{~N} / \mathrm{m}$
(B) $16 / 3 \mathrm{~N} / \mathrm{m}$
(C) $3 \mathrm{~N} / \mathrm{m}$
(D) $8 \mathrm{~N} / \mathrm{m}$

Dheeraj Sharma

Numerade Educator

Problem 33

A block of mass $2 \mathrm{~kg}$ is held over a vertical spring with spring unstretched. Suddenly, if block is left free, maximum compression of spring is [spring constant $K=200 \mathrm{~N} / \mathrm{m}]:$
(A) $0.2 \mathrm{~m}$
(B) $0.1 \mathrm{~m}$
(C) $0.4 \mathrm{~m}$
(D) $0.05 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 34

A block $m$ slides with a speed of $v_{0}=6 \mathrm{~m} / \mathrm{s}$ along a track from one level to a higher level as shown. The track is frictionless until the block reaches the higher level, where co-efficient of friction is $0.6$. The distance $d$ travelled by block on higher level before stopping is $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $\frac{7}{6} \mathrm{~m}$
(B) $\frac{5}{6} \mathrm{~m}$
(C) $\frac{29}{6} \mathrm{~m}$
(D) $3 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 35

In Fig. $4.20$ shown here, pulley and spring are ideal. If $k$ is spring constant of spring, the potential energy stored in it is $\left(m_{1}>m_{2}\right)$
Fig. $4.20$
(A) $\frac{2 m_{1}^{2} g^{2}}{k}$
(B) $\frac{2 m_{2}^{2} g^{2}}{k}$
(C) $\frac{\left(m_{1}+m_{2}\right)^{2} g^{2}}{k}$
(D) $\frac{1}{2} \frac{\left(m_{1}-m_{2}\right)^{2} g^{2}}{k}$

Dheeraj Sharma

Numerade Educator

Problem 36

Potential energy (in joule) of a particle of mass $1 \mathrm{~kg}$ moving in $x-y$ plane is $U=3 x+4 y$, here $x$ and $y$ are in meter. If at time $t=0$, particle is at rest at point $P(6 \mathrm{~m}$, $4 \mathrm{~m}$ ). Then
(A) acceleration of particle is $(3 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s}$.
(B) time when it crosses $y$-axis is $t=1 \mathrm{~s}$.
(C) speed of particle when it crosses $y$-axis is $10 \mathrm{~m} / \mathrm{s}$.
(D) it crosses $y$-axis at $y=-8 \mathrm{~m}$.

Dheeraj Sharma

Numerade Educator

Problem 37

A locomotive of mass $m$ starts moving so that its velocity varies as $v=\alpha s^{2 / 3}$, where $\alpha$ is a constant and $s$ is the distance traversed. The total work done by all the forces acting on the locomotive during the first $t$ second after the start of motion is
(A) $\frac{1}{8} m \alpha^{4} t^{2}$
(B) $\frac{m \alpha^{6} t^{4}}{162}$
(C) $\frac{m \alpha^{6} t^{4}}{81}$
(D) $\frac{m \alpha^{4} t^{2}}{2}$

Dheeraj Sharma

Numerade Educator

Problem 38

A vertical spring of force constant $100 \mathrm{~N} / \mathrm{m}$ is attached with a hanging mass of $10 \mathrm{~kg}$. Now an external force is applied on the mass so that the spring is stretched by additional $2 \mathrm{~m}$. The work done by the force $F$ is $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $200 \mathrm{~J}$
(B) $400 \mathrm{~J}$
(C) $450 \mathrm{~J}$
(D) $600 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 39

A body of mass $2 \mathrm{~kg}$ is moved from a point $A$ to a point $B$ by an external agent in a conservative force field. If the velocity of the body at the points $A$ and $B$ are $5 \mathrm{~m} / \mathrm{s}$ and $3 \mathrm{~m} / \mathrm{s}$, respectively, and the work done by the external agent is $-10 \mathrm{~J}$, then the change in potential energy between points $A$ and $B$ is
(A) $6 \mathrm{~J}$
(B) $36 \mathrm{~J}$
(C) $16 \mathrm{~J}$
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 40

A uniform chain has a mass $m$ and length $L .$ It is placed on a frictionless table with length $l_{0}$ hanging over the edge. The chain begins to slide down. The speed $v$ with which the chain slides away from the edge is given by
(A) $v=\sqrt{\frac{g l_{0}}{L}\left(L+l_{0}\right)}$
(B) $v=\sqrt{\frac{g l_{0}}{L}\left(L-l_{0}\right)}$
(C) $v=\sqrt{\frac{g}{L}\left(L^{2}-l_{0}^{2}\right)}$
(D) $v=\sqrt{2 g\left(L-l_{0}\right)}$

Dheeraj Sharma

Numerade Educator

Problem 41

In the adjoining Fig. 4.21, block $A$ is of mass $m$ and block $B$ is of mass $2 \mathrm{~m}$. The spring has a force constant $k$. All the surfaces are smooth and the system is released from rest with spring unstretched, then
(A) the maximum extension of the spring is $\frac{4 m g}{k}$.
(B) the speed of block $A$ when extension in spring is $\frac{2 m g}{k}$, is $2 g \sqrt{\frac{m}{k}}$
(C) the net acceleration of block $B$ when the extension in the spring is maximum, is $\frac{g}{2}$.
(D) tension in the thread for extension of $\frac{2 m g}{k}$ in spring is $m g$.

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 42

A spring is compressed between two toy carts of masses $m_{1}$ and $m_{2}$. When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same time $t$. If the coefficients of friction $\mu$ between the ground and the toy carts are equal, then the displacements of the toy carts are in the ratio
(A) $\frac{s_{1}}{s_{2}}=\frac{m_{2}}{m_{1}}$
(B) $\frac{s_{1}}{s_{2}}=\frac{m_{1}}{m_{2}}$
(C) $\frac{s_{1}}{s_{2}}=\left(\frac{m_{2}}{m_{1}}\right)^{2}$
(D) $\frac{s_{1}}{s_{2}}=\left(\frac{m_{1}}{m_{2}}\right)^{2}$

Dheeraj Sharma

Numerade Educator

Problem 43

A body of mass $m$ is dropped from a height $h$ on a sand floor. If the body penetrates $x \mathrm{~m}$ into the sand, the average resistance offered by the sand to the body is
(A) $m g\left(\frac{h}{x}\right)$
(B) $m g\left(1+\frac{h}{x}\right)$
(C) $m g h+m g x$
(D) $m g\left(1-\frac{h}{x}\right)$

Dheeraj Sharma

Numerade Educator

Problem 44

A block of mass $m$ is pulled by a constant power $P$ placed on a rough horizontal plane. The friction co-efficient between the block and surface varies with its speed $v$ as $\mu=\frac{1}{\sqrt{1+v}} .$ The acceleration of the block when its speed is $3 \mathrm{~m} / \mathrm{s}$ will be
(A) $\frac{P}{3 m}-\frac{g}{2}$
(B) $\frac{P}{3 m}+\frac{g}{2}$
(C) $\frac{P}{3 m}$
(D) $\frac{g}{2}$

Dheeraj Sharma

Numerade Educator

Problem 45

A block of mass $m$ is released from rest when the extension in the spring is $x_{0}$. The maximum downward displacement of the block is
(A) $\frac{m g}{2 k}-x_{0}$
(B) $\frac{m g}{2 k}+x_{0}$
(C) $\frac{2 m g}{k}-x_{0}$
(D) $\frac{2 m g}{k}+x_{0}$

Dheeraj Sharma

Numerade Educator

Problem 46

A small block of mass $m$ lying at rest at point $P$ of a wedge having a smooth semi-circular track of radius
$R$. What should be the minimum value of horizontal acceleration $a_{0}$ of wedge so that mass can just reach the point $Q$ ?
(A) $g / 2$
(B) $\sqrt{g}$
(C) $g$
(D) Not possible

Dheeraj Sharma

Numerade Educator

Problem 47

A bob is suspended from a crane by a cable of length $l=5 \mathrm{~m}$. The crane and the bob are moving at a constant speed $v_{0} .$ The crane is stopped by a bumper and the bob on the cable swings out an angle of $60^{\circ} .$ The initial speed $v_{0}$ is $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $10 \mathrm{~m} / \mathrm{s}$
(B) $7 \mathrm{~m} / \mathrm{s}$
(C) $4 \mathrm{~m} / \mathrm{s}$
(D) $2 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 48

A particle is moving with kinetic energy $E$, straight up an inclined plane with angle $\alpha$, the co-efficient of friction being $\mu$. The work done against friction, up to when the particle comes to rest, is
(A) $\frac{E \mu \cos \alpha}{\sin \alpha+\mu \cos \alpha}$
(B) $\frac{E \cos \alpha}{\sin \alpha+\mu \cos \alpha}$
(C) $\frac{E}{\sin \alpha+\mu \cos \alpha}$
(D) $\frac{E}{g(\sin \alpha+\mu \cos \alpha)}$

Dheeraj Sharma

Numerade Educator

Problem 49

A block of mass $m$ is pulled by a constant power $P$ placed on a rough horizontal plane. The friction co-efficient between the block and surface is $\mu$. The maximum velocity of the block is
(A) $\frac{P}{m g}$
(B) $\frac{P}{\mu m g}$
(C) $\frac{\mu P}{m g}$
(D) Infinite

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 50

A ball of mass $m$ is attached to a light string of length $L$ and suspended vertically. A constant horizontal force, whose magnitude $F$ equals the weight of the ball is applied. The speed of the ball as it reaches $90^{\circ}$ level is,
(A) $\sqrt{g L}$
(B) $\sqrt{2 g L}$
(C) $\sqrt{3 g L}$
(D) Zero

Dheeraj Sharma

Numerade Educator

Problem 51

A proton is kept at rest. A positively charged particle is released from rest at a distance $d$ in its field. Consider two experiments; one in which the charged particle is also a proton and in another, a position. In the same time $t$, the work done on the two moving charged particles is
(A) Same as the force law is involved in the two experiments.
(B) Less for the case of a positron, as the positron moves away more rapidly and the force on it weakens.
(C) More in the case of positron, as the positron moves away a larger distance.
(D) Same as the work done by charged particle on the stationary proton.

Mahendra K

Numerade Educator

Problem 52

A man squatting on the ground gets straight up and stands. The force of reaction of ground on the man during the process is
(A) Constant and equal to $\mathrm{mg}$ in magnitude.
(B) Constant is greater than $\mathrm{mg}$ in magnitude.
(C) Variable but always greater than $\mathrm{mg}$.
(D) At first greater than $\mathrm{mg}$ and later becomes equal to $\mathrm{mg}$.

Dheeraj Sharma

Numerade Educator

Problem 53

A bicyclist comes to a skidding stop in $10 \mathrm{~m}$. During this process, the force on the bicycle due to the road is $200 \mathrm{~N}$ and is directly opposed to the motion. The work done by the cycle on the road is
$(\mathrm{A})+2000 \mathrm{~J}$
(B) $-200 \mathrm{~J}$
(C) Zero
(D) $-20,000 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 54

A body is falling freely under the action of gravity alone in vaccum. Which of the following quantities remain constant during the fall?
(A) Kinetic energy
(B) Potential energy
(C) Total mechanical energy
(D) Total linear momentum

Dheeraj Sharma

Numerade Educator

Problem 55

During inelastic collision between two bodies, which of the following quantities always remain conserved?
(A) Total kinetic energy
(B) Total mechanical energy
(C) Total linear momentum
(D) Speed of each body

Dheeraj Sharma

Numerade Educator

Problem 56

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to
(A) $t^{3 / 4}$
(B) $t^{3 / 2}$
(C) $t^{1 / 4}$
(D) $t^{1 / 2}$

Dheeraj Sharma

Numerade Educator

Problem 57

Two springs have force constants, $K_{1}$ and $K_{2}\left(K_{1}>K_{2}\right)$ The work done, when both are stretched by the same amount of length will be
(A) Equal
(B) Greater for $K_{1}$
(C) Greater for $K_{2}$
(D) Given data is incomplete

Dheeraj Sharma

Numerade Educator

Problem 58

Choose the incorrect statement.
(A) No work is done on moving a block uniformly on a smooth horizontal table.
(B) Work done by earth's gravitational force on moon is zero, considering moon's orbit to be circular.
(C) No work is done by weight lifter holding a $175 \mathrm{~kg}$ mass steadily on his shoulder for $30 \mathrm{~s}$.
(D) Work done by frictional force is always negative.

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 59

A bob is suspended from a crane by a cable of length $l=5 \mathrm{~m}$. The crane and the bob are moving at a constant speed $v_{0}$. The crane is stopped by a bumper and the bob on the cable swings out an angle of $60^{\circ} .$ The initial speed $v_{0}$ is $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $10 \mathrm{~m} / \mathrm{s}$
(B) $7 \mathrm{~m} / \mathrm{s}$
(C) $4 \mathrm{~m} / \mathrm{s}$
(D) $2 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 60

When a body moves in a circle, the work done by the centripetal force is always
(A) $>0$
(B) $<0$
(C) Zero
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 61

A ball of mass $m$ is attached to the lower end of a light vertical spring of force constant $k$. The upper end of the spring is fixed. The ball is released from rest with the spring at its normal (unstretched) length and comes to rest again after descending through a distance $x$.
(A) $x=m g / k$
(B) $x=2 m g / k$
(C) The ball will have no acceleration at the position where it was descending through $x / 2$.
(D) The ball will have an upward acceleration equal to $g$ at its lowermost position.

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 62

A block of mass $2 \mathrm{~kg}$ is hanging over a smooth and light pulley through a light string. The other end of string is pulled by a constant force $F$. The kinetic energy of block increases by $16 \mathrm{~J}$ in $2 \mathrm{~s}$, then
(A) force $F$ may be $24 \mathrm{~N}$.
(B) force $F$ must be $24 \mathrm{~N}$.
(C) potential energy must be increase.
(D) potential energy may be increase.

Prem Bijarniya

Numerade Educator

Problem 63

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of
the particle. The motion of the particle takes place in a plane. It follows that
(A) its velocity is constant.
(B) its acceleration is constant.
(B) its kinetic energy is constant.
(D) it moves in a circular path.

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 64

A particle of mass $5 \mathrm{~kg}$ moving in the $X-Y$ plane has its potential energy given by $U=(-7 x+24 y)$ Joule. The particle is initially at origin and has velocity $\vec{u}=(14.4 \hat{i}+4.2 \hat{j}) \mathrm{m} / \mathrm{s}$
(A) The particle has speed $25 \mathrm{~m} / \mathrm{s}$ at $t=4 \mathrm{~s}$.
(B) The particle has an acceleration $5 \mathrm{~m} / \mathrm{s}^{2}$.
(C) The acceleration of particle is normal at its initial velocity.
(D) None of these.

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 65

Figure $4.22$ shows a massless spring fixed at the bottom end of an inclined of inclination $37^{\circ}\left(\tan 37^{\circ}=\right.$ $3 / 4$ ). A small block of mass $2 \mathrm{~kg}$ start slipping down the incline from a point $4.8 \mathrm{~m}$ away from free end of spring. The block compresses the spring by $20 \mathrm{~cm}$, stops momentarily and then rebounds through a distance $1 \mathrm{~m}$ up the inclined, then $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$.
(A) Coefficient of friction between block and inclined is $0.5$.
(B) Coefficient of friction between block and inclined is $0.75$.
(C) Value of spring constant is $1000 \mathrm{~N} / \mathrm{m}$.
69
(D) Value of spring constant is $2000 \mathrm{~N} / \mathrm{m}$.

Prem Bijarniya

Numerade Educator

Problem 66

A particle of mass $m$ is attached to a light string of length $l$, the other end of which is fixed. Initially, the string is kept horizontal and the particle is given an upward velocity $v$. The particle is just able to complete a circle.
(A) The string becomes slack when the particle reaches its highest point.
(B) The velocity of the particle becomes zero at the highest point.
(C) The kinetic energy of the ball in initial position was $\frac{1}{2} m v^{2}=m g l$.
(D) The particle again passes through the initial position.

Prem Bijarniya

Numerade Educator

Problem 67

A particle of mass $5 \mathrm{~kg}$ moving in the $X-Y$ plane has its potential energy given by $U=(-7 x+24 y)$ Joule. The particle is initially at origin and has velocity $\vec{u}=(14.4 \hat{i}+4.2 \hat{j}) \mathrm{m} / \mathrm{s}$
(A) The particle has speed $25 \mathrm{~m} / \mathrm{s}$ at $t=4 \mathrm{~s}$.
(B) The particle has an acceleration $5 \mathrm{~m} / \mathrm{s}^{2}$.
(C) The acceleration of particle is normal to its initial velocity.
(D) None of these.

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 68

One end of a light spring of spring constant $k$ is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is $\frac{1}{2} k x^{2}$. The possible cases are:
(A) The spring was initially compressed by a distance $x$ and was finally in its natural length.
(B) It was initially stretched by a distance $x$ and finally was in its natural length.
(C) It was initially in its natural length and finally in a compressed position.
(D) It was initially in its natural length and finally in a stretched position.

Prem Bijarniya

Numerade Educator

Problem 69

The co-efficient of friction between the block and plank is $\mu$ and its value is such that block becomes stationary with respect to plank before it reaches the other end. Then
(A) the work done by friction on the block is negative.
(B) the work done by friction on the plank is positive.
(C) the net work done by friction is negative.
(D) net work done by the friction is zero.

Prem Bijarniya

Numerade Educator

Problem 70

Potential energy associated with a conservative force is given by $U=A x^{2}$, where $A$ is a constant then
(A) force always tends to accelerate the particle towards origin.
(B) force always tends to accelerate the particle away from origin.
(C) force always tends to accelerate the particle towards the origin if $A$ is positive.
(D) force always tends to accelerate the particle away from origin if $A$ is negative.

Prem Bijarniya

Numerade Educator

Problem 71

The speed of the ball when it is at an angular position of $\theta$ with respect to vertical
(A) $\sqrt{\frac{10 g}{7}[h-r+R)+(R-r) \cos \theta}$
(B) $\sqrt{\frac{10 g}{7}[(h-R)+(R-r) \cos \theta}$
(C) $\sqrt{\frac{5 g}{7}[h-(r+R)+(R-r \cos \theta)}$
(D) $\sqrt{\frac{5 g}{7}[h-(R+r)(1-\cos \theta)}$

Hunza Gilgit

Numerade Educator

Problem 72

Frictional force acting on the ball as it passes through point $Y$ is
(A) Change its direction from left to right.
(B) Changes its direction from right to left.
(C) Does not change its direction.
(D) Not zero at point $Y$.

Prabhu Ramji

Numerade Educator

Problem 73

The friction force plays a role in energy transformation as
(A) It converts the gravitational potential energy into rotational KE only.
(B) It converts the gravitational potential energy into translational KE only.
(C) It has no role in energy transformation.
(D) None of these.

Prabhu Ramji

Numerade Educator

Problem 74

How much work does the person do against the gravitational force daily?
(A) $25 \mathrm{~kJ}$
(B) $50 \mathrm{~kJ}$
(C) $10 \mathrm{~kJ}$
(D) $75 \mathrm{~kJ}$

Prabhu Ramji

Numerade Educator

Problem 75

How much energy does fat supply each day?
(A) $5 \times 10^{4} \mathrm{~J}$
(B) $2.5 \times 10^{5} \mathrm{~J}$
(C) $8 \times 10^{6} \mathrm{~J}$
(D) $4 \times 10^{6} \mathrm{~J}$

Prabhu Ramji

Numerade Educator

Problem 76

How much fat will the person use up in 10 days?
(A) $6.25 \times 10^{-2} \mathrm{~kg}$
(B) $12.5 \times 10^{-2} \mathrm{~kg}$
(C) $25 \times 10^{-2} \mathrm{~kg}$
(D) $3.125 \times 10^{-2} \mathrm{~kg}$

Prabhu Ramji

Numerade Educator

Problem 77

The direction in which force $(F=13 \mathrm{~N})$ is applied is at
(A) $90^{\circ}$ with the direction of motion of the train.
(B) $\cos ^{-1} \frac{5}{13}$ with the direction of motion of the train.
(C) $\cos ^{-1} \frac{5}{12}$ with the direction of motion of the train.
(D) $\cos ^{-1} \frac{12}{13}$ with the direction of motion of the train.

Prem Bijarniya

Numerade Educator

Problem 78

The magnitude of acceleration of the particle with respect to the ground at $t=5 \mathrm{~s}$ is
(A) $\sqrt{61} \mathrm{~m} / \mathrm{s}^{2}$
(B) $\sqrt{72} \mathrm{~m} / \mathrm{s}^{2}$
(C) $\sqrt{8} \mathrm{~m} / \mathrm{s}^{2}$
(D) $6 \mathrm{~m} / \mathrm{s}^{2}$

Prem Bijarniya

Numerade Educator

Problem 79

The momentum of the particle at $t=6 \mathrm{~s}$ with respect to the train is
(A) $12 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$
(B) $10 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$
(C) $6 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$
(D) $8 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$

Prem Bijarniya

Numerade Educator

Problem 80

The kinetic energy of the particle at $t=20 \mathrm{~s}$ with respect to the ground is
(A) $5 \times 10^{3} \mathrm{~J}$
(B) $6 \times 10^{3} \mathrm{~J}$
(C) $8 \times 10^{3} \mathrm{~J}$
(D) $7 \times 10^{3} \mathrm{~J}$

Prem Bijarniya

Numerade Educator

Problem 81

The speed of small length $(d x)$ at a distance $x$ from fixed end is
(A) $\frac{x}{L} v$
(B) $v$
(C) $\frac{L}{x} v$
(D) $x v$

Prem Bijarniya

Numerade Educator

Problem 82

Kinetic energy of the spring
(A) $\frac{1}{2} m v^{2}$
(B) $\frac{1}{6} m v^{2}$
(C) $m v^{2}$
(D) $\frac{1}{4} m v^{2}$

Prem Bijarniya

Numerade Educator

Problem 83

Ball's speed when the spring reaches its uncompressed length is
(A) $3.9 \mathrm{~m} / \mathrm{s}$
(B) $6.1 \mathrm{~m} / \mathrm{s}$
(C) $14 \mathrm{~m} / \mathrm{s}$
(D) $1.62 \mathrm{~m} / \mathrm{s}$

Prem Bijarniya

Numerade Educator

Problem 84

Calculate the magnitude of work done on the tool by $\vec{F}$. If this displacement is along the straight line $y=x$ that connects these two points.
(A) $2.50 \mathrm{~J}$
(B) $500 \mathrm{~J}$
(C) $50.6 \mathrm{~J}$
(D) $2 \mathrm{~J}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 85

Calculate the work done on the tool by $\vec{F}$ of the tool is first moved out along the $x$-axis to the point $x=3.00 \mathrm{~m}, y=0$ and then moved parallel to the $y$-axis to $x=3.00 \mathrm{~m}, y=3.00 \mathrm{~m}$
(A) $67.5 \mathrm{~J}$
(B) $85 \mathrm{~J}$
(C) $102 \mathrm{~J}$
(D) $7.5 \mathrm{~J}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 86

What can you predict about $\vec{F}$ ?
(A) Force is non-conservative.
(B) Force is conservative.
(C) Force is neitherconservative nor non-conserva
(D) Data insufficient to conclude.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 87

The displacement-time $(x-t)$ graph of a body acted upon by some forces is shown in Fig. $4.23$.
(A) For $O A$, the total work
(1) Positive done by all the forces together is
(B) For $A B$ acceleration is
(2) Negative
(C) From $O$ to $B$ velocity is
(3) First positive, then negative
(D) At $B$ acceleration is
(4) First negative, then positive
(5) Zero

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 88

A projectile is launched at angle $\theta$ to the horizontal from $O$ and it hits the target $P$ on level ground.
(A) Magnitude of radial
(1) Increases acceleration
(B) Magnitude of
(2) Can be negative tangential acceleration
(C) Power delivered by
(3) First increases, gravity then decrease
(D) Rate of change of
(4) First decreases, $\begin{array}{ll}\text { speed of projectile } & \text { then increases }\end{array}$ with respect to time

Joy Chugh

Numerade Educator

Problem 89

In the following columns: Column-I some types of potential energies are given and in Column-II some possible values of these potential energies are given. Match the following:
(A) Electrostatic potential energy
(1) Positive
(B) Gravitational potential
(2) Negative energy
(C) Elastic potential energy
(3) Zero
(D) Magnetic potential energy
(4) Not defined

Prabhu Ramji

Numerade Educator

Problem 90

In Fig. $4.24, m_{1}=8 \mathrm{~kg}, m_{2}=16 \mathrm{~kg}, K=100 \mathrm{~N} / \mathrm{m}$,
$\mu=0.2$
(A) The minimum value of $F$ 12
(in N) in order to shift the block of mass $m_{1}$ is
$\begin{array}{ll}\text { (B) Negative of work done by } & \text { (2) } 40\end{array}$ friction (in J) on block $B$ till this moment is
(C) Work done by $F$ till this
(3) Zero moment
(D) The minimum value of $F$
(4) 32 in order to shift the block of mass $m_{2}$ if it is applied on $A$.
(5) $6.4$

Prem Bijarniya

Numerade Educator

Problem 91

A block of mass $2 \mathrm{~kg}$ is released from rest on a smooth inclined plane of inclination $30^{\circ}$ and connected by a massless spring of force constant $1000 \mathrm{~N} / \mathrm{m}$ as shown in Fig. $4.25$. Initially, the spring is in its natural length. An external variable force also acts on the block down the inclined plane. Block comes to rest for a moment
after travelling a distance of $20 \mathrm{~cm}$ along the inclined plane. From initial to this moment, Column-I gives work done by various forces and Column-II gives their values.
(A) Work done by gravity
(1) Zero
(B) Work done by spring
(2) $18 \mathrm{~J}$
(C) Work done by external force
(3) $-20 \mathrm{~J}$
(D) Work done by normal force
(4) $2 \mathrm{~J}$
(5) $20 \mathrm{~J}$

Prem Bijarniya

Numerade Educator

Problem 92

Assertion: Work done by a force in a certain interval of time may not depend on initial velocity. Reason: Work done by a force is frame-dependent.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\overline{\mathrm{C}}$
(D) D

Prem Bijarniya

Numerade Educator

Problem 93

Assertion: Friction force is a non-conservative force.
Reason: When a body is moved on a rough surface in a closed path, the work done by friction force is zero.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Prabhu Ramji

Numerade Educator

Problem 94

Assertion: Static frictional force may be greater than kinetic frictional force.

Reason: Static frictional force is always equal to $\mu_{s} N$ $(N=$ normal reaction $)$
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\overline{\mathrm{C}}$
(D) D

Prabhu Ramji

Numerade Educator

Problem 95

Assertion: For stable equilibrium, force has to be zero and potential energy should be minimum. Reason: For equilibrium, it is not necessary that force is not zero.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Prabhu Ramji

Numerade Educator

Problem 96

Assertion: Work done by frictional force on a sphere rolling without slipping on an inclined plane is negative.
Reason: Work done by the force $F, W=\int \vec{F} \cdot d \vec{S}$
(A) A
(B) $\mathrm{B}$
(C) C
(D) D

Prabhu Ramji

Numerade Educator

Problem 97

Assertion: Work done by friction force may be positive. Reason: Force of friction always opposes relative motion.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Prabhu Ramji

Numerade Educator

Problem 98

Assertion: Work done by spring force is always negative. Reason: In compression or stretching of a spring from its natural length, work is done on the spring against the restoring force.
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Prabhu Ramji

Numerade Educator

Problem 99

Assertion: When force retards the motion of a body, the work done is zero. Reason: Work done depends on angle between force and displacement.
(A) $\mathrm{A}$
(B) $\underline{B}$
(C) $\mathrm{C}$
(D) D

Prabhu Ramji

Numerade Educator

Problem 100

Assertion: Total mechanical energy of the system can never be greater than potential energy.
Reason: If non-conservative forces perform negative work, then mechanical energy of the system decreases.
(A) $\mathrm{A}$
(B) $\underline{B}$
(C) $\mathrm{C}$
(D) D

Prem Bijarniya

Numerade Educator

Problem 101

Assertion: A body at rest can possess mechanical energy. Reason: A body at rest cannot possess kinetic energy with respect to an inertial frame.
(A) A
(B) B
(C) $\mathrm{C}$
(D) D

Prabhu Ramji

Numerade Educator

Problem 102

A mass $m=1 \mathrm{~kg}$ moving horizontally with velocity $v_{0}=2 \mathrm{~m} / \mathrm{s}$ collides in elastically with a pendulum of same mass. Find the maximum change in potential energy (in Joule) of combined mass.

Dheeraj Sharma

Numerade Educator

Problem 103

A block of mass $0.5 \mathrm{~kg}$ is kept in an elevator moving down with an acceleration $2 \mathrm{~m} / \mathrm{s}^{2}$. Find the magnitude work done (in Joule) by the normal contact force on the block in first second. Initially system is at rest $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

Dheeraj Sharma

Numerade Educator

Problem 104

State principle of conservation of mechanical energy. A block of mass $2 \mathrm{~kg}$ moving with speed $2 \mathrm{~m} / \mathrm{s}$ compresses a spring through a distance $20 \mathrm{~cm}$ before its speed is halved. The value of spring constant is $75 \mathrm{~N}$ then the value of $\mathrm{N}$ is ?

Dheeraj Sharma

Numerade Educator

Problem 105

A $1 \mathrm{~kg}$ block collides with a horizontal light spring of force constant $2 \mathrm{~N} / \mathrm{m}$. The maximum compression in the spring is $4 \mathrm{~m}$. Assuming that co-efficient of kinetic friction between the block and the horizontal surface is $0.25$, what is initial speed of the block (approx.)?

Dheeraj Sharma

Numerade Educator

Problem 106

A truck of mass $2000 \mathrm{~kg}$ has a velocity of $8 \mathrm{~ms}^{-1}$ when it starts from a point $A$ to descend a slope $A B$, $200 \mathrm{~m}$ long shown in the Fig. $4.26$. The truck arrives at $B$ which is $18 \mathrm{~m}$ below the level of $A$ with a velocity of $20 \mathrm{~ms}^{-1} .$ The resistance in Newton offered is $40 x$, find the value of $x ?$ (given $g=10 \mathrm{~ms}^{-1}$ )

Dheeraj Sharma

Numerade Educator

Problem 107

Two identical beads of $m=100 \mathrm{~g}$ are connected by an inextensible massless string that can slide along the
two arms $A C$ and $B C$ of a rigid smooth wireframe in a vertical plane. If the system is released from rest, the kinetic energy of the first particle when they have moved by a distance of $0.1 \mathrm{~m}$ is $16 x \times 10^{-3} \mathrm{~J}$. Find the value of $x .\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

Dheeraj Sharma

Numerade Educator

Problem 108

Two blocks $A$ and $B$ of equal mass $m=1 \mathrm{~kg}$ are lying on a smooth horizontal surface as shown in Fig. $4.27$. A spring of force constant $K=200 \mathrm{~N} / \mathrm{m}$ is fixed at one end of block $A$. Block $B$ collides with another end of the spring with velocity $v_{0}=2 \mathrm{~m} / \mathrm{s}$. What will be the maximum compression of the spring? [in decimeter $]$

Dheeraj Sharma

Numerade Educator

Problem 109

One end of an unstretched springs of force constant $k_{1}$ is attached to the ceiling of an elevator. A block of mass $1.5 \mathrm{~kg}$ is attached to other end. Another spring of force constant $k_{2}$ is attached to the bottom of the mass and to the floor of the elevator as shown in Fig. 4.28. At equilibrium, the deformation in both the spring are equal and is $40 \mathrm{~cm}$. If the elevator moves with constant acceleration upward, the additional deformation in both the springs have $8 \mathrm{~cm}$. Find the elevator's acceleration $\left(g=10 \mathrm{~ms}^{-2}\right)$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 110

A system consists of two identical cubes, each of mass $3 \mathrm{~kg}$, linked together by a compressed weightless spring of force constant $1000 \mathrm{~N} / \mathrm{m}$. The cubes are also connected by a thread which is burnt at a certain moment. At what minimum value of initial compression, $x_{0}$ (in $\mathrm{cm}$ ) of the spring will the lower cube bounce up after the thread is burnt through?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 111

A homogeneous rope of mass per unit length $\lambda$ and length $l$ kept on ground and one end of the rope is fixed to ground at $O .$ The left end of the rope (with respect to fixed end) is pulled by an external agent which imparts constant velocity $v$ to it. Find the work done by the external agent (in joule) to place the moving end extremely right with respect to fixed end. Take $\lambda=1 \mathrm{~kg} / \mathrm{m}, v=1 \mathrm{~ms}^{-1}$ and $l=1 \mathrm{~m}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 112

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to $[2003]$
(A) $t^{3 / 4}$
(B) $t^{3 / 2}$
(C) $t^{1 / 4}$
(D) $t^{1 / 2}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 113

A spring of spring constant $5 \times 10^{3} \mathrm{~N} / \mathrm{m}$ is stretched initially by $5 \mathrm{~cm}$ from the unstretched position. Then the work required to stretch it further by another $5 \mathrm{~cm}$ is $[\mathbf{2 0 0 3}]$
(A) $12.50 \mathrm{~N} / \mathrm{m}$
(B) $18.75 \mathrm{~N} / \mathrm{m}$
(C) $25.00 \mathrm{~N} / \mathrm{m}$
(D) $6.25 \mathrm{~N} / \mathrm{m}$

Dheeraj Sharma

Numerade Educator

Problem 114

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200 \mathrm{~N}$ to the lower end. The weight stretches the wire by $1 \mathrm{~mm}$. Then the elastic energy stored in the wire is $[\mathbf{2 0 0 3}]$
(A) $0.2 \mathrm{~J}$
(B) $10 \mathrm{~J}$
(C) $20 \mathrm{~J}$
(D) $0.1 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 115

Consider the following two statements:
[2003]
A: Linear momentum of a system of particles is zero B: Kinetic energy of a system of particles is zero. Then
(A) A does not imply $\mathbf{B}$ and $\mathbf{B}$ does not imply $\mathbf{A}$
(B) A implies $\mathbf{B}$ but $\mathbf{B}$ does not imply $\mathbf{A}$
(C) $\mathbf{A}$ does not imply $\mathbf{B}$ but $\mathbf{B}$ implies $\mathbf{A}$
(D) A implies $\mathbf{B}$ and $\mathbf{B}$ implies $\mathbf{A}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 116

A force $\vec{F}=(5 \hat{i}+3 \hat{j}+2 \hat{k}) \mathrm{N}$ is applied over a particle which displaces it from its origin to the point $\vec{r}=(2 \hat{i}-\hat{j}) m .$ The work done on the particle in joules is
(A) $+10$
(B) $+7$
(C) $-7$
(D) $+13$

Dheeraj Sharma

Numerade Educator

Problem 117

A uniform chain of length $2 \mathrm{~m}$ is kept on a table such that a length of $60 \mathrm{~cm}$ hangs freely from the edge of the table. The total mass of the chain is $4 \mathrm{~kg}$. What
is the work done in pulling the entire chain on the table?
(A) $12 \mathrm{~J}$
(B) $3.6 \mathrm{~J}$
(C) $7.2 \mathrm{~J}$
(D) $1200 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 118

A particle moves in a straight line with retardation proportion to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to [2004]
(A) $x$
(B) $e^{x}$
(C) $x^{2}$
(D) $\log _{e} x$

Dheeraj Sharma

Numerade Educator

Problem 119

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle; the motion of the particle takes place in a plane. It follows that
(A) Its kinetic energy is constant.
(B) Its acceleration is constant.
(C) Its velocity is constant.
(D) It moves in a straight line.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 120

A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1} .$ The instantaneous power delivered to the body as a function of time $t$ is [2004]
(A) $\frac{m v_{1} t^{2}}{t_{1}}$
(B) $\frac{m v_{1}^{2} t}{t_{1}^{2}}$
(C) $\frac{m v_{1} t}{t_{1}}$
(D) $\frac{m v_{1}^{2} t}{t_{1}}$

Dheeraj Sharma

Numerade Educator

Problem 121

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $t$. The instantaneous power delivered to the body as a function of time is given by
(A) $\frac{m v^{2}}{t^{2}} t^{2}$
(B) $\frac{m v^{2}}{t^{2}} t$
$[2005]$
(C) $\frac{1}{2} \frac{m v^{2}}{t^{2}} t^{2}$
(D) $\frac{1}{2} \frac{m v^{2}}{t^{2}} t$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 122

A spherical ball of mass $20 \mathrm{~kg}$ is stationary at the top of a hill of height $100 \mathrm{~m}$. It rolls down a smooth surface to the ground, then climbs up another hill of height $30 \mathrm{~m}$ and finally rolls down to a horizontal base at a height of $20 \mathrm{~m}$ above the ground. The velocity attained by the ball is
(A) $20 \mathrm{~m} / \mathrm{s}$
(B) $40 \mathrm{~m} / \mathrm{s}$
(C) $10 \sqrt{30} \mathrm{~m} / \mathrm{s}$
(D) $10 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 123

The block of mass $m$ moving on the frictionless horizontal surface collides with the spring of spring constant $k$ and compresses it by length $L$. The maximum momentum of the block after collision is $[\mathbf{2 0 0 5}]$
(A) $\frac{k L^{2}}{2 m}$
(B) $\sqrt{m k} L$
(C) $\frac{m L^{2}}{k}$
(D) Zero

Dheeraj Sharma

Numerade Educator

Problem 124

The potential energy of a $1 \mathrm{~kg}$ particle free to move along the $x$-axis is given by $V(x)=\left(\frac{x^{4}}{4}-\frac{x^{2}}{2}\right) \mathrm{J}$. The total mechanical energy of the particle is $2 \mathrm{~J}$. Then, the maximum speed (in $\mathrm{m} / \mathrm{s}$ ) is [2006]
(A) $\frac{3}{\sqrt{2}}$
(B) $\sqrt{2}$
(C) $\frac{1}{\sqrt{2}}$
(D) 2

Dheeraj Sharma

Numerade Educator

Problem 125

A particle of mass $100 \mathrm{~g}$ is thrown vertically upwards with a speed of $5 \mathrm{~m} / \mathrm{s}$. The work done by the force of gravity during the time the particle goes up is [2006]
(A) $-0.5 \mathrm{~J}$
(B) $-1.25 \mathrm{~J}$
(C) $1.25 \mathrm{~J}$
(D) $0.5 \mathrm{~J}$

Vysakh M

Numerade Educator

Problem 126

A $2 \mathrm{~kg}$ block slides on a horizontal floor with a speed of $4 \mathrm{~m} / \mathrm{s}$. It strikes an uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is $15 \mathrm{~N}$ and spring constant is $10,000 \mathrm{~N} / \mathrm{m}$. The spring compresses by $[\mathbf{2 0 0 7}]$
(A) $8.5 \mathrm{~cm}$
(B) $5.5 \mathrm{~cm}$
(C) $2.5 \mathrm{~cm}$
(D) $11.0 \mathrm{~cm}$

Vysakh M

Numerade Educator

Problem 127

A block of mass $0.50 \mathrm{~kg}$ is moving with a speed of $2.00 \mathrm{~ms}^{-1}$ on a smooth surface. It strikes another mass of $1.00 \mathrm{~kg}$ and then they move together as a single body. The energy loss during the collision is
(A) $0.16 \mathrm{~J}$
(B) $1.00 \mathrm{~J}$
(C) $0.67 \mathrm{~J}$
(D) $0.34 \mathrm{~J}$

Vysakh M

Numerade Educator

Problem 128

An athlete in the Olympic Games covers a distance of $100 \mathrm{~m}$ in $10 \mathrm{~s}$. His kinetic energy can be estimated to be in the range [2008]
(A) $200 \mathrm{~J}-500 \mathrm{~J}$
(B) $2 \times 10^{5} \mathrm{~J}-3 \times 10^{5} \mathrm{~J}$
(C) $20,000 \mathrm{~J}-50,000 \mathrm{~J}$
(D) $2,000 \mathrm{~J}-5,000 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 129

The potential energy function for the force between two atoms in a diatomic molecule is approximately given as $U(x)=\frac{a}{x^{12}}-\frac{b}{x^{6}}$, where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D=\left[U(x=\infty)-U_{\text {at equilibrium }} D\right.$ is $\quad$ [2010]
(A) $\frac{b^{2}}{2 a}$
(B) $\frac{b^{2}}{12 a}$
(C) $\frac{b^{2}}{4 a}$
(D) $\frac{b^{2}}{6 a}$

Vysakh M

Numerade Educator

Problem 130

This question has Statement 1 and Statement $2 .$ Of the four choices given after the statements, choose the one that best describes the two statements.

If two springs $S_{1}$ and $S_{2}$ of force constants $k_{1}$ and $k_{2}$, respectively, are stretched by the same force, it is found that more work is done on spring $S_{1}$ than on spring $S_{2}$ Statement 1: If stretched by the same amount, work done on $S_{1}$ will be more than that on $S_{2}$ Statement $2: k_{1}<k_{2}$
$[\mathbf{2 0 1 2}]$
(A) Statement 1 is false, Statement 2 is true.
(B) Statement 1 is true, Statement 2 is false
(C) Statement 1 is true, Statement 2 is true and Statement 2 is the correct explanation for Statement 1
(D) Statement 1 is true, Statement 2 is true and Statement 2 is not the correct explanation of Statement 1

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 131

When a rubber band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=a x+$ $b x^{2}$, where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is:
[2014]
(A) $a L^{2}+b L^{3}$
(B) $\frac{1}{2}\left(a L^{2}+b L^{3}\right)$
(C) $\frac{a L^{2}}{2}+\frac{b L^{3}}{3}$
(D) $\frac{1}{2}\left(\frac{2 L^{2}}{2}+\frac{b L^{2}}{3}\right)$

Vysakh M

Numerade Educator

Problem 132

A person trying to lose weight by burning fat lifts a mass of $10 \mathrm{~kg}$ up to a height of $1 \mathrm{~m} 1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^{7} \mathrm{~J}$ of energy per $\mathrm{kg}$, which is converted into mechanical energy with a $20 \%$ efficiency rate. Take $g=9.8 \mathrm{~ms}^{-2}$ : $\quad$ [2016]
(A) $6.45 \times 10^{-3} \mathrm{~kg}$
(B) $9.89 \times 10^{-3} \mathrm{~kg}$
(C) $12.89 \times 10^{-3} \mathrm{~kg}$
(D) $2.45 \times 10^{-3} \mathrm{~kg}$

Dheeraj Sharma

Numerade Educator

Problem 133

A point particle of mass $m$ moves along the uniformly rough track PQR as shown in the Fig. $4.29$. The coefficient of friction, between the particle and the rough track equals. The particle is released, from rest, from the point $P$ and it comes to rest at a point $R$. The energies, lost by the ball, over the parts, $P Q$ and $Q R$, of
the track, are equal to each other, and no energy is lost when particle changes direction from $P Q$ to $Q R$.

The values of the coefficient of friction and the distance $x(=Q R)$, are, respectively close to:
$[2016]$
(A) $0.2$ and $3.5 \mathrm{~m}$
(B) $0.29$ and $3.5 \mathrm{~m}$
(C) $0.29$ and $6.5 \mathrm{~m}$
(D) $0.2$ and $6.5 \mathrm{~m}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator