Arihant AIEEE Physics

D.B. Singh

Chapter 6

Work, Energy and Power - all with Video Answers

Educators

Chapter Questions

Problem 1

A lorry and a car, moving with the same $\mathrm{KE}$ are brought to rest by applying the same retarding force then:
(a) lorry will come to rest in a shorter distance
(b) car will come to rest in a shorter distance
(c) both will come to rest in the same distance
(d) none of the above

Mahendra K

Mahendra K

Numerade Educator

Problem 2

In a certain situation, $\mathbf{F}$ and $\vec{s}$ are not equal to zero but the work done is zero. From this, we conclude that:
$\rightarrow \quad \rightarrow$
(a) $\mathbf{F}$ and $\vec{s}$ are in same direction
(b) $\overrightarrow{\mathrm{F}}$ and $\overrightarrow{\mathrm{s}}$ are perpendicular to each other $\Rightarrow$
(c) $\mathrm{F}$ and $\overrightarrow{\mathrm{s}}$ are in opposite direction
(d) none of the above

Mahendra K

Numerade Educator

Problem 3

A gas expands from 5 litre to 205 litre at a constant pressure $50 \mathrm{~N} / \mathrm{m}^{2}$. The work done is :
(a) $2000 \mathrm{~J}$
(b) $1000 \mathrm{~J}$
(c) $10000 \mathrm{~J}$
(d) none of these

Mahendra K

Numerade Educator

Problem 4

A flywheel of mass $60 \mathrm{~kg}$, radius $40 \mathrm{~cm}$ is revolving 300 revolutions per min. Its kinetic energy will be :
(a) $480 \pi^{2} \mathrm{~J}$
(b) $48 \mathrm{~J}$
(c) $48 \pi J$
(d) $\frac{4}{\pi} J$

Mahendra K

Numerade Educator

Problem 5

A constant force of $5 \mathrm{~N}$ is applied on a block of mass 20 $\mathrm{kg}$ for a distance of $2.0 \mathrm{~m}$, the kinetic energy acquired by the block is:
(a) $20 \mathrm{~J}$
(b) $15 \mathrm{~J}$
(c) $10 \mathrm{~J}$
(d) $5 \mathrm{~J}$

Mahendra K

Numerade Educator

Problem 6

Under the action of a force, a $2 \mathrm{~kg}$ body moves such that its position $x$ as function of time $t$ is given by $x=\frac{t^{3}}{3}$ where $x$ is in metre and $t$ is in sec, the work done by the force in first two sec is:
(a) $16 \mathrm{~J}$
(b) $32 \mathrm{~J}$
(c) $8 \mathrm{~J}$
(d) 64 J

Mahendra K

Numerade Educator

Problem 7

The momentum of a body of mass $5 \mathrm{~kg}$ is $10 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$. A force of $2 \mathrm{~N}$ acts on the body in the direction of motion for $5 \mathrm{sec}$, the increase in the kinetic energy is:
(a) $15 \mathrm{~J}$
(b) $50 \mathrm{~J}$
(c) $30 \mathrm{~J}$
(d) none of these

Mahendra K

Numerade Educator

Problem 8

A block of mass $5 \mathrm{~kg}$ slides down a rough inclined surface. The angle of inclination is $45^{\circ}$. The coefficient of sliding friction is $0.20$. When the block slides $10 \mathrm{~m}$, the work done on the block by force of friction is:
(a) $50 \sqrt{2} \mathrm{~J}$
(b) $-50 \sqrt{2} \mathrm{~J}$
(c) $50 \mathrm{~J}$
(d) $-50 \mathrm{~J}$

Mahendra K

Numerade Educator

Problem 9

A particle moves along the $x$ -axis from $x=0$ to $x=5 \mathrm{~m}$ under the influence of a force given by $F=7-2 x+3 x^{2}$ The work dune in the process is:
(a) $70 \mathrm{~J}$
(b) $270 \mathrm{~J}$
(c) $35 \mathrm{~J}$
(d) $135 \mathrm{~J}$

Mahendra K

Numerade Educator

Problem 10

A $2 \mathrm{~kg}$ brick of dimension $5 \mathrm{~cm} \times 2 . \mathrm{cm} \times 1.5 \mathrm{~cm}$ is lying on the largest base. It is now $\mathrm{m}^{\text {*de to }}$ stand with length vertical, then the amount ut work done is: (taken $g=10 \mathrm{~m} / \mathrm{s}^{2}$
(a) $35 \mathrm{~J}$
(b) $5 \mathrm{~J}$
(c) $7 \mathrm{~J}$
(d) $9 \mathrm{~J}$

Mahendra K

Numerade Educator

Problem 11

A bomb of $12 \mathrm{~kg}$ explodes into two pieces of masses $4 \mathrm{~kg}$ and $8 \mathrm{~kg}$. The velocity of $8 \mathrm{~kg}$ mass is $6 \mathrm{~m} / \mathrm{s}$. The kinetic energy of other mass is:
(a) $48 \mathrm{~J}$
(b) $32 \mathrm{~J}$
(c) $24 \mathrm{~J}$
(d) $288 \mathrm{~J}$

Mahendra K

Numerade Educator

Problem 12

A torque equal to $\left(\frac{5}{\pi}\right) \times 10^{-6} \mathrm{Nm}$ acting on a body produces 2 revolutions per second, then the rotational power expended is:
(a) $\frac{1}{\pi} \times 10^{-5} \mathrm{~J} / \mathrm{s}$
(b) $2 \times 10^{-\bar{j}} \mathrm{~J} / \mathrm{s}$
(c) $2.5 \pi \times 10^{-6} \mathrm{~J} / \mathrm{s}$
(d) $\frac{2 \pi}{5} \times 10^{-8} \mathrm{~J} / \mathrm{s}$

Mahendra K

Numerade Educator

Problem 13

A coolie $1.5 \mathrm{~m}$ tall raises a load of $80 \mathrm{~kg}$ in $2 \mathrm{sec}$ from the ground to his head and then walks a distance of $40 \mathrm{~m}$ in another 2 second. The power developed by the coolie is: $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $0.2 \mathrm{~kW}$
(b) $0.4 \mathrm{~kW}$
(c) $0.6 \mathrm{~kW}$
(d) $0.8 \mathrm{~kW}$

Mahendra K

Numerade Educator

Problem 14

A lorry of mass $2000 \mathrm{~kg}$ is travelling up a hill of certain height at a constant speed of $10 \mathrm{~m} / \mathrm{s}$. The frictional resistance is $200 \mathrm{~N}$, then the power expended by the engine is approximately: (take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(a) $22 \mathrm{~kW}$
(b) $220 \mathrm{~kW}$
(c) $2000 \mathrm{~W}$
(d) none of these

Mahendra K

Numerade Educator

Problem 15

A spring of force constant $10 \mathrm{~N} / \mathrm{m}$ has initial stretch $0.2 \mathrm{~m}$. In changing the stretch to $0.25 \mathrm{~m}$, the increase of PE is about :
(a) $0.1 \mathrm{~J}$
(b) $0.2 \mathrm{~J}$
(c) $0.3 \mathrm{~J}$
(d) $0.5 \mathrm{~J}$

Mahendra K

Numerade Educator

Problem 16

Sand falls vertically at the rate of $2 \mathrm{~kg} / \mathrm{s}$ on to a conveyer belt moving horizontaliy with velocity of $0.2 \mathrm{~m} / \mathrm{s}$, the extro voiver required to keep the belt moving is:(a) $0.08 \mathrm{~W}$
(b) $0.04 \mathrm{~W}$
(c) $4 \mathrm{~W}$
(d) $1 \mathrm{~W}$

Mahendra K

Numerade Educator

Problem 17

Ten litre of water per second is lifted from well through $20 \mathrm{~m}$ and delivered with a velocity of $10 \mathrm{~m} / \mathrm{s}$, then the power of the motor is:
(a) $1.5 \mathrm{~kW}$
(b) $2.5 \mathrm{~kW}$
(c) $3.5 \mathrm{~kW}$
(d) $4.5 \mathrm{~kW}$

Mahendra K

Numerade Educator

Problem 18

A bomb of mass $M$ at rest explodes into two fragments of masses $m_{1}$ and $m_{2}$. The total energy released in the explosion is $E$. If $E_{1}$ and $E_{2}$ represent the energies carried by masses $m_{1}$ and $m_{2}$ respectively, then which of the following is correct?
(a) $E_{1}=\frac{m_{2}}{M} E$
(b) $E_{1}=\frac{m_{1}}{m_{2}} E$
(c) $E_{1}=\frac{m_{1}}{M} E$
(d) $E_{1}=\frac{m_{2}}{m_{1}} E$

Mahendra K

Numerade Educator

Problem 19

The earth's radius is $R$ and acceleration due to gravity at its surface is $g$. If a body of mass $m$ is sent to a height $h=\frac{R}{5}$ from the earth's surface, the potential energy increases by :
(a) $m g h$
(b) $\frac{4}{5} m g h$
(c) $\frac{5}{6} m g h$
(d) $\frac{6}{7} m g h$

Mahendra K

Numerade Educator

Problem 20

At a certain instant, a body of mass $0.4 \mathrm{~kg}$ has a velocity of $(8 \hat{i}+b \hat{j}) \mathrm{m} / \mathrm{s}$. The kinetic energy of the body is:
(a) $10 \mathrm{~J}$
(b) $40 \mathrm{~J}$
(c) $20 \mathrm{~J}$
(d) none of these

Mahendra K

Numerade Educator

Problem 21

A chain of mass $M$ is placed on a smooth table with $1 / 3$ of its length $L$ hanging over the edge. The work done in pulling the chain back to the surface of the table is:
(a) $\frac{\mathrm{Mg} L}{3}$
(b) $\frac{M g L}{6}$
(c) $\frac{\mathrm{MgL}}{9}$
(d) $\frac{M g L}{18}$

Mahendra K

Numerade Educator

Problem 22

When a man increases his speed by $2 \cdot \mathrm{m} / \mathrm{s}$, he finds that his kinetic energy is doubled, the original speed of the man is:
(a) $2(\sqrt{2}-1) \mathrm{m} / \mathrm{s}$
(b) $2(\sqrt{2}+1) \mathrm{m} / \mathrm{s}$
(c) $4.5 \mathrm{~m} / \mathrm{s}$
(d) none of these

Mahendra K

Numerade Educator

Problem 23

Two springs $A$ and $B$ are stretched by applying forces of equal magnitudes at the four ends. If spring constant is 2 times greater than that of spring constant $B$, and the energy stored in $A$ is $E$, that in $B$ is :
(a) $E / 2$
(b) $2 E$
(c) $E$
(d) $\frac{E}{4}$

Mahendra K

Numerade Educator

Problem 24

A block of mass $m$ slides from the rim of a hemispherical bowl of radius $R$. The velocity of the block at the bottom will be :
(a) $\sqrt{R g}$
(b) $\sqrt{2 R g}$
(c) $\sqrt{2 \pi R g}$
(d) $\sqrt{\pi R g}$

Mahendra K

Numerade Educator

Problem 25

A glass ball is dropped from height $10 \mathrm{~m}$. If there is $20 \%$ loss of energy due to impact, then after one impact, the ball will go upto:
(a) $2 \mathrm{~m}$
(b) $4 \mathrm{~m}$
(c) $6 \mathrm{~m}$
(d) $8 \mathrm{~m}$

Mahendra K

Numerade Educator

Problem 26

A moving neutron collides with a stationary $\alpha$ particle. The fraction of the kinetic energy lost by the neutron is:(a) $16 / 25$
(b) $9 / 25$
(c) $3 / 5$
(d) $2 / 5$

Mahendra K

Numerade Educator

Problem 27

A stone of mass $2 \mathrm{~kg}$ is projected upward with KE of $98 \mathrm{~J}$. The height at which the KE of the body becomes half its original value, is given by: (take $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ )
(a) $5 \mathrm{~m}$
(b) $2.5 \mathrm{~m}$
(c) $1.5 \mathrm{~m}$
(d) $0.5 \mathrm{~m}$

Mahendra K

Numerade Educator

Problem 28

A body of mass $10 \mathrm{~kg}$ is moving on a horizontal surface by applying a force of $10 \mathrm{~N}$ in forward direction. If body moves with constant velocity, the work done by applied force for a displacement of $2 \mathrm{~m}$ is :
(a) 20 joule
(b) 10 joule
(c) 30 joule
(d) 40 joule

Mahendra K

Numerade Educator

Problem 29

In previous problem Q. (1), the work done by force of friction is :
(a) $-20$ joule
(b) 10 joule
(c) 20 joule
(d) $-5$ joule

Mahendra K

Numerade Educator

Problem 30

In previous problem Q. (1), the work done by normal reaction is :
(a) 20 joule
(b) 196 joule
(c) zero
(d) none of these

Mahendra K

Numerade Educator

Problem 31

A body of mass $10 \mathrm{~kg}$ is moving on an inclined plane of inclination $30^{\circ}$ with an acceleration $2 \mathrm{~m} / \mathrm{s}^{2}$. The body starts from rest. The work done by force of gravity in 2 second is:
(a) 10 joule
(b) zero
(c) 98 joule
(d) 196 joule

Mahendra K

Numerade Educator

Problem 32

In previous problem Q. (4), the work done by force of friction is :
(a) $-58$ joule
(b) 58 joule
(c) 98 joule
(d) $-116$ joule

Mahendra K

Numerade Educator

Problem 33

A body of mass $1 \mathrm{~kg}$ moves from point $A(2 \mathrm{~m}, 3 \mathrm{~m}, 4 \mathrm{~m})$ to $B(3 \mathrm{~m}, 2 \mathrm{~m}, 5 \mathrm{~m})$. During motion of body, a force $\vec{F}=(2 N) \hat{i}-(4 N) \hat{j}$ acts on it. The work done by the force on the particle during displace- ment is :
(a) $2 \hat{i}-4 \hat{j}$ joule
(b) 2 joule
(c) $-2$ joule
(d) none of these

Mahendra K

Numerade Educator

Problem 34

A force $F=A y^{2}+B y+C$ acts on a body in the $y$ -direction. The work done by this force during a displacement from $y=-a$ to $y=a$ is :
(a) $\frac{2 A a^{3}}{3}$
(b) $\frac{2 A a^{3}}{3}+2 C a$
(c) $\frac{2 A a^{3}}{3}+\frac{B a^{2}}{2}+C a$
(d) none of these

Mahendra K

Numerade Educator

Problem 35

A force $\vec{F}=-k(y \hat{i}+x \hat{j})$ (where $k$ is a positive constant) acts on a particle moving in the $x-y$ plane starting from the origin, the particle is taken along the positive $x$ -axis to the point $(a, 0)$ and the parallel to the $y$ -axis to the point $(a, a)$. The total work done by the force $\overrightarrow{\mathbf{F}}$ on the particle is:(a) $-2 \mathrm{ka}^{2}$
(b) $2 \mathrm{ka}^{2}$
(c) $-\mathrm{ka}^{2}$
(d) $\mathrm{ka}^{2}$

Mahendra K

Numerade Educator

Problem 36

During swinging of simple pendulum :
(a) the work done by gravitational force is zero
(b) the work done by tension force is always zero
(c) the mechanical energy of bob does not remain constant in the absence of air
(d) the mechanical energy remains constant in the presence of air resistance

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 37

If a man having bag in his hand moves up on a stair, then:
(a) the work done by lifting force is zero
(b) the work done by lifting force is non-zero with respect to ground
(c) the work done by lifting force is zero with respect to ground
(d) the work done with respect to ground is same as that with respect to him

Mahendra K

Numerade Educator

Problem 38

Work done during raising a box on to a platform:
(a) depends upon how fast it is raised
(b) does not depend upon how fast it is raised
(c) does not depend upon mass of the box
(d) both (a) and (b) are correct

Mahendra K

Numerade Educator

Problem 39

A Swimmer swims upstream at rest with respect to the shore:
(a) in the mechanical sense, he does not perform work
(b) in physical sense, he does not perform work
(c) in the mechanical sense, he may perform work
(d) in physical sense, he may perform work

Mahendra K

Numerade Educator

Problem 40

A force of $0.5 \mathrm{~N}$ is applied on upper block as shown in figure. The work done by lower block on upper block for a displacement $3 \mathrm{~m}$ of the upper block is :
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )(a) 1 joule
(b) $-1$ joule
(c) 2 joule
(d) $-2$ joule

Mahendra K

Numerade Educator

Problem 41

In previous problem, work done by lower block on upper block in the frame of lower block is:
(a) $-1$ joule
(b) $-2$ joule
(c) 2 joule
(d) zero

Mahendra K

Numerade Educator

Problem 42

In previous problem, work done by upper block on lover block is :
(a) 1 joule
(b) $-1$ joule
(c) $-2$ joule
(d) 2 joule

Mahendra K

Numerade Educator

Problem 43

A body of mass $m$ was slowly halved upon the hill by a force which at each point was directed along a tangent to the path. The work done by the applied force:(a) does not depend upon path followed by the body
(b) depends upon path(c) does not depend upon position of $A$ and $B$
(d) both (a) and (c) are correct

Mahendra K

Numerade Educator

Problem 44

In an elastic string whose natural length is equal to that of a uniform rod be attached to the rod at both ends and suspended by the middle point:
(a) the rod will sink until the total work done is non-zero
(b) the rod will sink intil the total work done is zero
(c) sinking of rod is not determined on, the basis of work done
(d) sinking of rod is not possible

Mahendra K

Numerade Educator

Problem 45

A particle moves along a curve of unknown shape but magnitude of force $F$ is constant and always acts along tangent to the curve. Then :
(a) $\overrightarrow{\text { F }}$ may be conservative
(b) $\vec{F}$ must be conservative
(c) $\overrightarrow{\mathbf{F}}$ may be non-conservative
(d) $\overrightarrow{\mathbf{F}}$ must be non-conservative

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 46

If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane $\overrightarrow{\mathbf{F}}=\overrightarrow{\mathbf{x}}+\overrightarrow{\mathrm{y}} \mathbf{i}$, then
(a) $\overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathrm{dr}}=x d x+y d y$
(b) $\int \overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathrm{dr}} \neq \frac{1}{2} m v^{2}$
(c) $\overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathrm{d} \mathbf{r}} \neq x d x \times y d y$
(d) $\frac{1}{2} m v^{2} \neq \int(x d x+y d y)$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 47

If $c$ is a closed curve, then for conservative force $\overrightarrow{\mathbf{F}}$ :
(a) $\phi \overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{d}} \neq 0$
(b) $\oint \vec{F} \cdot \overrightarrow{d r}<0$
(c) $\oint_{e}^{c} \overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathrm{d} r}>0$
(d) $\oint \overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{d}} \mathrm{r}=0$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 48

Which of the following is /are not conservative force?
(a) Gravitational force
(b) Electrostatic force in the coulomb field
(c) Frictional force
(d) All of the above

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 49

If $\overrightarrow{\mathbf{F}}=F_{x} \hat{\mathrm{i}}+F_{y} \hat{j}+F_{z} \hat{\mathbf{k}}$ is conservative, then :
(a) $\frac{\partial F_{\underline{x}}}{\partial y}=\frac{\partial F_{v}}{\partial x} \frac{\partial F_{y}}{\partial z}=\frac{\partial F_{2}}{\partial y} \frac{\partial F_{z}}{\partial x}=\frac{\partial F_{x}}{\partial z}$
(b) $\frac{\partial F_{x}}{\partial y} \neq \frac{\partial F_{u}}{\partial x}$
(c) $\frac{\partial F_{x}}{\partial y}+\frac{\partial F_{u}}{\partial x}-\frac{\partial F_{z}}{\partial z}$
(d) none of the above

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 50

If a man of mass $M$ jumps to the ground from a height $h$ and his centre of mass moves a distance $x$ in the time taken by him to hit the ground, the average force acting on him is:
(a) $\frac{M g h}{x}$
(b) $\frac{M g x}{h}$
(c) $M g\left(\frac{h}{x}\right)^{2}$
(d) $M g\left(\frac{x}{h}\right)^{2}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 51

The potential energy of a particle of mass $0.1 \mathrm{~kg}$ moving along the $x$ -axis is given by $U=5 x(x-4) J$, where $x$ is in metre. It can be concluded that:
(a) the particle is acted upon by a constant force
(b) the speed of the particle is maximum at $x=2 \mathrm{~m}$
(c) the particle cannot execute simple harmonic motion
(d) the period of oscillation of the particle is $\frac{\pi}{20} \mathrm{~s}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 52

The potential energy as a function of 'the force between two atoms in a diatomic molecule is given by $U(x)=\frac{a}{x^{12}}-\frac{b}{6}$ where $a$ and $b$ are positive constants and $x$ is the distance between the atoms. The position of stable equilibrium for the system of the two atoms is given by:
(a) $x=\frac{d}{b}$
(b) $x=\sqrt{\frac{a}{b}}$
(c) $x=\frac{\sqrt{3 a}}{b}$
(d) $x=\sqrt[6]{\left(\frac{2 a}{b}\right)}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 53

The potential energy of a particle of mass $5 \mathrm{~kg}$ moving in the $x-y$ plane is given by $U=(-7 x+24 y)$ J. $x$ and $y$ being in meter. If the particle starts from rest from origin then speed of particle at $t=2 \mathrm{sec}$ is:
(a) $5 \mathrm{~m} / \mathrm{s}$
(b) $14 \mathrm{~m} / \mathrm{s}$
(c) $17.5 \mathrm{~m} / \mathrm{s}$
(d) $10 \mathrm{~m} / \mathrm{s}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 54

The potential energy of a particle of mass $5 \mathrm{~kg}$ moving in the $x-y$ plane is given by $U=-7 x+24 y$ joule, $x$ and $y$ being in metre. Initially at $t=0$ the particle is at the origin. $(0,0)$ moving with a velocity of $6[2.4 \hat{\mathrm{i}}+0.7 \hat{\mathrm{j}}]$ $\mathrm{m} / \mathrm{s}$. The magnitude of force on the particle is:
(a) 25 units
(b) 24 units
(c) 7 units
(d) none of these

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 55

Which one of the following units measures energy?
(a) kilo-watt-hour
(b) $(\mathrm{vol} \mathrm{t})^{2}(\mathrm{sec})^{-1}(\mathrm{ohm})^{-1}$
(c) (pascal) (foot) $^{-}$
id) none of the above

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 56

A balloon is rising from the surface of earth. Then its potential energy :
(a) increases
(b) decreases
(c) first increases then decreases
(d) remains constant

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 57

If a compressed spring is dissolved in acid:
(a) the energy of the spring increases
(b) the energy of acid decreases
(c) the potential energy and kinetic energy of molecule of acid increases
(d) the temperature of acid decreases

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 58

Two identical cylindrical shape vessels are placed, $A$ at ground and $B$ at height $h$. Each contains liquid of density $\rho$ and the heights of liquid in $A$ and $B$ are $h_{1}$ and $h_{2}$ respectively. The area of either base is $A$. The total potential energy of liquid system with respect to ground is:
(a) $\frac{A p g}{2}\left(h_{1}^{2}+h_{2}^{2}+2 h h_{2}\right)$
(b) $\frac{A \rho g}{2}\left(h_{1}+h_{2}\right)^{2}+h_{2}^{2}$
(c) $h \cdot A p g\left(h_{1}+h+h_{2}\right)$
(d) $\frac{A p g}{2}\left(\frac{h_{1}+h}{2}\right)+h_{2}^{2}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 59

A long spring, when stretched by $x \mathrm{~cm}$ has a potential energy $U$. On increasing the length of spring by stretching to $n x \mathrm{~cm}$, the potential energy stored in the spring will be:
(a) $\frac{U}{!}$
(b) $n U$
(c) $n^{2} U$
(d) $\frac{U}{n^{2}}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 60

Two identical cylindrical shape vessels are placed, $A$ at ground and $B$ at height $h$. Each contains liquid of density $\rho$ and the heights of liquid in $A$ and $B$ are $h_{1}$ and $h_{2}$ respectively. The area of either base is $A$. The total potential energy of liquid system with respect to ground is:
(a) $\frac{A p g}{2}\left(h_{1}^{2}+h_{2}^{2}+2 h h_{2}\right)$
(b) $\frac{A \rho g}{2}\left(h_{1}+h_{2}\right)^{2}+h_{2}^{2}$
(c) $h \cdot A p g\left(h_{1}+h+h_{2}\right)$
(d) $\frac{A p g}{2}\left(\frac{h_{1}+h}{2}\right)+h_{2}^{2}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 61

A long spring, when stretched by $x \mathrm{~cm}$ has a potential energy $U$. On increasing the length of spring by stretching to $n x \mathrm{~cm}$, the potential energy stored in the spring will be:
(a) $\frac{U}{!}$
(b) $n U$
(c) $n^{2} U$
(d) $\frac{U}{n^{2}}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 62

Two identical massless springs $A$ and $B$ consist spring constant $k_{A}$ and $k_{B}$ respectively. Then:
(a) if they are compressed by same force, work done on $A$ is more expanded when $k_{A}>k_{B}$
(b) if they are compressed by same amount, work done on $A$ is more expanded when $k_{A}<k_{B}$
(c) if they are compressed by same amount, work done on $A$ is more expanded when $k_{A}>k_{B}$
(d) both (a) and (b) are correct

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 63

Mark correct option:
(a) The negative change in potential energy is equal to work done
(b) Mechanical energy of a system remains constant
(c) If internal forces are non-conservative, the net work done by internal forces must be zero
(d) None of the above

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 64

A point mass $m$ is released from rest on an undeformed massless spring of force constant $k$. Which of the following graphs represents $U-x$ graph for reference level of gravitational potential energy at initial position ?

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 65

In the above problem:
(a) first the point mass decelerates then accelerates
(b) first the point mass accelerates then decelerates(c) at the maximum compression of spring, acceleration of mass is zero
(d) the point mass moves with constant velocity

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 66

An object kept on a smooth inclined plane of height 1 unit and length $l$ can be kept stationary relative to inclined plane by a horizontal acceleration equals to :
(a) $\frac{8}{\sqrt{l^{2}-1}}$
(i) $\frac{g}{\sqrt{1^{2}+1}}$
(c) $\frac{1}{g \sqrt{l^{2}-1}}$
(d) $g \sqrt{1^{2}-1}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 67

The work done on a particle is equal to the change in its kinetic energy :
(a) always
(b) only if the force acting on the body are conservative
(c) only if the forces acting on the body are gravitational
(d) only if the forces acting on the body are elastic

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 68

If a car is moving on a straight road with constant speed, then :
(a) work is done against force of fricticn
(b) net work done on car is zero
(c) net work done may be zero
(d) both (a) and (b) are correct

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 69

The kinetic energy of a particle moving on a curved path continuously increases with time. Then:
(a) resultant force on the particle must be parallel to the velocity at all instants
(b) the resultant force on the particle must be at an angle less than $90^{\circ}$ all the time
(c) its height above the ground level must continuously decrease
(d) the magnitude of its linear momentum is increasing continuously
(e) both (b) and (d) are correct

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 70

Force $F$ acts on a body of mass $1 \mathrm{~kg}$ moving with an initial velocity $v_{0}$ for $1 \mathrm{sec}$. Then :
(a) distance covered by the body is $v_{0}+\frac{F}{2}$
(b) final velocity of body is $\left(v_{0}+F\right)$
(c) momentum of body is increased by $F$
(d) all of the above

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 71

A block of mass $m$ is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force $F$. The kinetic energy of the block increases by $20 \mathrm{~J}$ in $1 \mathrm{~s}$ is :
(a) the tension in the string is $m g$
(b) the tension in the string is $F$
(c) the work done by the tension on the block is $20 \mathrm{~J}$ in the above $1 \mathrm{~s}$
(d) the work done by the force of gravity is $20 \mathrm{~J}$ in the above 1 s

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 72

When a bullet of mass $10 \mathrm{~g}$ and speed $100 \mathrm{~m} / \mathrm{s}$ penetrates up to distance $1 \mathrm{~cm}$ in a human body in rest. The resistance offered by human body is :
(a) $2000 \mathrm{~N}$
(b) $1500 \mathrm{~N}$
(c) $5000 \mathrm{~N}$
(d) $1000 \mathrm{~N}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 73

A $60 \mathrm{~g}$ bullet is fired through a stack of fibre board sheet, $200 \mathrm{~mm}$ thick. If the bullet approaches the stack with a velocity of $600 \mathrm{~m} / \mathrm{s}$, the average resistance offered to the bullet is :
(a) $54 \mathrm{kN}$
(b) $2 \mathrm{kN}$
(c) $20.25 \mathrm{kN}$
(d) $10 \mathrm{kN}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 74

In the given curved road, if particle is released from $A$ then:
(a) kinetic energy at $B$ must be $m g h$
(b) kinetic energy at $B$ may be zero
(c) kinetic energy at $B$ must be less than $m g h$
(d) kinetic energy at $B$ must not be equal to zero

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 75

A bucket tied to a string is lowered at a constant acceleration of $\frac{g}{4}$. If the mass of the bucket is $m$ and is lowered by a distance $d$, the work done by the string will be:
(a) $\frac{m g d}{4}$
(b) $-\frac{3}{4} m g d$
(c) $-\frac{4}{3} m g d$
(d) $\frac{4}{3} m g d$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 76

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is :
(a) $\sqrt{u^{2}-2 g L}$
(b) $\sqrt{2 g L}$
(c) $\sqrt{u^{2}-g L}$
(d) $\sqrt{2\left(u^{2}-g L\right)}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 77

A small sphere of mass $m$ is suspended by a thread of length $l$. It is raised upto the height of suspension with thread fully stretched and released. Then the maximum tension in thread will be:
(a) $\overline{m g}$
(b) $2 m g$
(c) $3 m g$
(d) $6 \mathrm{mg}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 78

An object of mass $m$ is tiec to a string of length $L$ anc
a variable horizontal forc is applied on it which starts at zero an gradually increases unti the string makes an angl
\theta with the vertical. Worl done by the force $F$ is:(a) $m g L(1-\sin \theta)$
(b) $m g L$
(c) $m g L(1-\cos \theta)$
(d) $m g L(1+\cos \theta)$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 79

An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x .$ It is further stretched by another small length $y$. The work done inthe second stretching is :
(a) $\frac{1}{2} k y^{2}$
(b) $\frac{1}{2} k\left(x^{2}+y^{2}\right)$
(c) $\frac{1}{2} k(x+y)^{2}$
(d) $\frac{1}{2} k y(2 x+y)$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 80

An insect is crawling up a fixed hemispherical bowl of radius $R$. The coefficient of friction between insect and
bowl is $\frac{1}{3}$. The insect can only crawl upto a height:
(a) $60 \%$ of $R$
(b) $10 \%$ of $R$
(c) $5 \%$ of $R$
(d) $100 \%$ of $R$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 81

Two small balls of equal mass are joined by a light rigid rod. If they are released from rest in the position shown and slide on the smooth track in the vertical plane. The speed of balls when $A$ reaches $B$ 's position and $B$ is at $B^{\prime}$ is :(a) $4 \mathrm{~m} / \mathrm{s}$
(b) $4.21 \mathrm{~m} / \mathrm{s}$
(c) $2.21 \mathrm{~m} / \mathrm{s}$
(d) none of these

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 82

In the given figure, the natural length of spring is $0.4 \mathrm{~m}$ and spring constant is $200 \mathrm{~N} / \mathrm{m}$. The $3 \mathrm{~kg}$ slider and attached spring are released from rest at end move in the vertical plane. The slider comes in rest at the point $B$. The work done by the friction during motion of slider is:(a) $-3.52 \mathrm{~J}$
(b) $-0.8 \mathrm{~J}$
(c) $-100 \mathrm{~J}$
(d) - 10.54 J

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 83

Power is :
(a) the time derivative of force
(b) the time derivative of kinetic energy
(c) the distance derivative of work
(d) the distance derivative of force

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 84

A man weighing $60 \mathrm{~kg}$ climbs a staircase carrying a 20 kg load on his hand. The staircase has 20 steps and eacl step has a height of $20 \mathrm{~cm}$. If he takes 20 second to climb his power is:
(a) $160 \mathrm{~W}$
(b) $230 \mathrm{~W}$
(c) $320 \mathrm{~W}$
(d) $80 \mathrm{~W}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 85

The average human heart forces four litre of blood per minute through arteries a pressure of $125 \mathrm{~mm}$. If the density of blood is $1.03 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, then the power o heart is :
(a) $112.76 \times 10^{-6} \mathrm{HP}$
(b) $112.76$ HP
(c) $1.03 \times 10^{\overline{3}} \mathrm{HP}$
(d) $1.03 \times 10^{-6} \mathrm{HP}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 86

An object of mass $M$, initially at rest under the action of a constant force $F$ attains a velocity $v$ in time $t$. Then the average power supplied to the mass is :
(a) $\mathrm{Fv}$
(b) $\frac{1}{2} F v$
(c) zero
(d) $\frac{m v^{2}}{2 t}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 87

The power supplied by a force acting on a particle moving in a straight line is constant. The velocity of the particle varies with the displacement $x$ as:
(a) $\sqrt{x}$
(b) $x$
(c) $x^{2}$
(d) $x^{1 / 3}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 88

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_{c}$ is varying with time $t$ as $a_{c}=k^{2} r t^{2}$. The power is:(a) $2 \pi m k^{2} r^{2} t$
(b) $m k^{2} r^{2} t$
(c) $\frac{m k^{4} r^{2} t^{5}}{3}$
(d) zero

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 88

A wind powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy for wind speed $v$, the electrical power output will be proportional to:
(a) $v$
(b) $v^{2}$
(c) $v^{3}$
(d) $v^{4}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 89

A particle moves with a velocity $(5 \hat{i}-3 \hat{j}+6 \hat{k}) \mathrm{m} / \mathrm{s}$ under the influence of a constant force $\overrightarrow{\mathbf{F}}=10 \hat{\mathrm{i}}+10^{-1}+20 \hat{\mathrm{k}} \mathrm{N}$. The instantaneous power applied
to the particle is
(a) $200 \mathrm{~J} / \mathrm{sec}$
(b) $40 \mathrm{~J} / \mathrm{sec}$
(c) $140 \mathrm{~J} / \mathrm{sec}$
(d) $170 \mathrm{~J} / \mathrm{sec}$

Dharmendra Jain

Dharmendra Jain

Numerade Educator