Master Resource Book in JEE Main Physics

D. B. Singh

Chapter 7

Work, Energy and Power - all with Video Answers

Educators

Section 1

Round 1

Problem 1

Under the action of a force, a $2 \mathrm{~kg}$ body moves such that its position $x$ as a function of time $t$ is given by $x=t^{3} / 3$, where $x$ is in metre and $t$ in second. The work done by the force in the first two seconds is
(a) $1.6 \mathrm{~J}$
(b) $16 \mathrm{~J}$
(c) $160 \mathrm{~J}$
(d) $1600 \mathrm{~J}$

Dheeraj Sharma

Dheeraj Sharma

Numerade Educator

Problem 2

The work done in pulling up a block of wood weighing $2 \mathrm{kN}$ for a length of $10 \mathrm{~m}$ on a smooth plane inclined at an angle of $15^{\circ}$ with the horizontal is $\left[\sin 15^{\circ}=0.2588\right]$
(a) $4.36 \mathrm{~kJ}$
(b) $5.13 \mathrm{k}]$
(c) $8.91 \mathrm{~kJ}$
(d) $9.82 \mathrm{~kJ}$

Dheeraj Sharma

Numerade Educator

Problem 3

A mass $M$ is lowered with the help of a string by a distance $h$ at a constant acceleration $g / 2 .$ The work done by the string will be
(a) $\frac{M g h}{2}$
(b) $\frac{-M g h}{2}$
(c) $\frac{3 M g h}{2}$
(d) $\frac{-3 M g h}{2}$

Dheeraj Sharma

Numerade Educator

Problem 4

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another.
This is because, $\quad$ [NCERT Exemplar]
(a) the two magnetic forces are equal and opposite, so they produce no net effect
(b) the magnetic forces do no work on each particle
(c) the magnetic forces do equal and opposite (but non-zero) work on each particle
(d) the magnetic forces are necessarily negligible

Dheeraj Sharma

Numerade Educator

Problem 5

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 the force and the ball goes upto $2 \mathrm{~m}$ height further. Find the magnitude of force (Consider $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(a) $22 \mathrm{~N}$
(b) $4 \mathrm{~N}$
(c) $16 \mathrm{~N}$
(d) $20 \mathrm{~N}$

Dheeraj Sharma

Numerade Educator

Problem 6

A $5 \mathrm{~kg}$ brick of $20 \mathrm{~cm} \times 10 \mathrm{~cm} \times 8 \mathrm{~cm}$ dimensionless lying on the largest base. It is now made to stand with length vertical. If $g=10 \mathrm{~ms}^{-2}$, then the amount of work done is
(a) $3 \mathrm{~J}$
(b) $5 \mathrm{~J}$
(c) 7$]$
(d) $9 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 7

A block of mass $10 \mathrm{~kg}$ slides down a rough slope which is inclined at $45^{\circ}$ to the horizontal. The coefficient of sliding friction is $0.30$. When the bloek has slide $5 \mathrm{~m}$, the work done on the block by the force of friction is nearly
(a) $115 \mathrm{~J}$
(b) $75 \sqrt{2} \mathrm{~J}$
(c) $321.4 \mathrm{~J}$
(d) $-321.4 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 8

In a children's park, there is a slide which has a total length of $10 \mathrm{~m}$ and a height of $8.0 \mathrm{~m}$. A vertical ladder is provided to reach the top. A boy weighing $200 \mathrm{~N}$ climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the slide is three-tenth of his weight. The work done by the slide on the boy as he comes down is
$\begin{array}{lll}\text { (a) zero } & \text { (b) }+600 \mathrm{~J} & \text { (c) }-600 \mathrm{~J}\end{array}$
(d) $+1600 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 9

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 positron. In the same time $t$, the work done on the two moving charged particles is
(a) same as the same force law is involved in the experiments
(b) less for the case of a positron, as the positron moves away more rapidly and the force on it weakness.
(c) more for the case of a positron, as the positron moves away a larger distance
(d) same as the work done by charged particle on the stationary proton

Dheeraj Sharma

Numerade Educator

Problem 10

A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during the process is $\quad$ [NCERT Exemplar]
(a) constant and equal to $m g$ in magnitude
(b) constant and greater than $m g$ in magnitude
(c) variable but always greater than $\mathrm{mg}$
(d) at first greater than $m g$, and later becomes equal to $m g$

Dheeraj Sharma

Numerade Educator

Problem 11

A ball is released from the top of a tower. The ratio of work done by force of gravity in Ist second, 2nd second and 3 rd second of the motion of ball is
(a) $1: 2: 3$
(b) $1: 4: 16$
(c) $1: 3: 5$
(d) $1: 9: 25$

Dheeraj Sharma

Numerade Educator

Problem 12

A plate of mass $m$, length $b$ and breadth $a$ is initially lying on a horizontal floor with length parallel to the floor and breadth perpendicular to the floor. The work done to erect it on its breadth is
(a) $m g\left[\frac{b}{2}\right]$
(b) $m g\left[a+\frac{b}{2}\right]$
(c) $m g\left[\frac{b-a}{2}\right]$
(d) $m g\left[\frac{b+a}{2}\right]$

Dheeraj Sharma

Numerade Educator

Problem 13

The displacement $x$ in metre of a particle of mass $m \mathrm{~kg}$ moving in one dimension under the action of a force is related to the time $t$ in second by the equation $t=\sqrt{x}+3$, the work done by the force (in joule) in first. six seconds is
(a) $18 \mathrm{~m}$
(b) zero
(c) $9 \mathrm{~m} / 2$
(d) $36 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 14

A position-dependent force $F=3 x^{2}-2 x+7$ acts on a body of mass $7 \mathrm{~kg}$ and displaces it from $x=0 \mathrm{~m}$ to $x=5 \mathrm{~m}$. The work done on the body is $x^{\prime}$ joule. If both $F$ and $x$ are measured in SI units, the value of $x^{\prime}$ is
(a) 135
(b) 235
(c) 335
(d) 935

Dheeraj Sharma

Numerade Educator

Problem 15

A body of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity, $v=a x^{3 / 2}$, where $a=5 \mathrm{~m}^{-1 / 2} / \mathrm{s}$. What is the work done by the net force during its displacement from $x=0$ to $x=2 \mathrm{~m} ?$
(a) $30 \mathrm{~J}$
(b) $40 \mathrm{~J}$
(c) $20 \mathrm{~J}$
(d) $50 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 16

A uniform chain of length $L$ and mass $M$ overhangs a horizontal table with its two-third part on the table. The friction coefficient between the table and the chain is $\mu$. The work done by the friction during the period the chain slips off the table is
(a) $-\frac{1}{4} \mu \mathrm{Mg} \mathrm{L}$
(b) $-\frac{2}{9} \mu \mathrm{Mgl}$
(c) $-\frac{4}{9} \mu \mathrm{Mg} L$
(d) $-\frac{6}{7} \mu \mathrm{Mg} L$

Dheeraj Sharma

Numerade Educator

Problem 17

A $5 \mathrm{~kg}$ stone of relative density 3 is resting at the bed of a lake. It is lifted through a height of $5 \mathrm{~m}$ in the lake. If $g=10 \mathrm{~ms}^{-2}$, then the work done is
(a) $\frac{500}{3} \mathrm{~J}$
(b) $\frac{350}{3} \mathrm{~J}$
(c) $\frac{750}{3} \mathrm{~J}$
(d) zero

Dheeraj Sharma

Numerade Educator

Problem 18

A force acts on a $30 \mathrm{~g}$ particle in such a way that the position of the particle as function of time is given by $x=3 t-4 t^{2}+t^{3}$, where $x$ is in metre and $t$ is in second. The work done during the first 4 seconds is
(a) 5.28 J
(b) $450 \mathrm{~mJ}$
(c) $490 \mathrm{~m} \mathrm{~J}$
(d) $530 \mathrm{~mJ}$

Dheeraj Sharma

Numerade Educator

Problem 19

A car weighing $1400 \mathrm{~kg}$ is moving at a speed of $54 \mathrm{kmh}^{-1}$ up a hill when the motor stops. If it is just able to reach the destination which is at a height of $10 \mathrm{~m}$ above the point, then the work done against friction (negative of the work done by the friction) is (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $10 \mathrm{~kJ}$
(b) $15 \mathrm{~kJ}$
(c) $17.5 \mathrm{~kJ}$
(d) $25 \mathrm{~kJ}$

Dheeraj Sharma

Numerade Educator

Problem 20

A cord is used to lower vertically a block of mass $M$ by
a distance $d$ with constant downward acceleration $g / 4$ work done by the cord on the block is
(a) $M g \frac{d}{4}$
(b) $3 M g \frac{d}{4}$
(c) $-3 M g \frac{d}{4}$
(d) $\mathrm{Mgd}$

Dheeraj Sharma

Numerade Educator

Problem 21

Water is drawn from a well in a $5 \mathrm{~kg}$ drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is $0.5 \mathrm{kgm}^{-1}$. The work done in lifting water to the ground from the surface of water in the well $20 \mathrm{~m}$ below is $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $1.4 \times 10^{4} \mathrm{~J}$
(b) $1.5 \times 10^{4} \mathrm{~J}$
(c) $9.8 \times 10 \times 6 \mathrm{~J}$
(d) $18 . \mathrm{J}$

Dheeraj Sharma

Numerade Educator

Problem 22

A wire of length $L$ suspended vertically from a rigid support is made to suffer extension $l$ in its length by applying a force $F$. The work is
(a) $\frac{F l}{2}$
(b) $F l$
(c) $2 \mathrm{Fl}$
(d) $\mathrm{Fl}$

Dheeraj Sharma

Numerade Educator

Problem 23

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 $\quad$ [NCERT Exemplar]
(a) $+2000 \mathrm{~J}$
(b) - $200 \mathrm{~J}$
(c) zero
(d) $-20,000 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 24

A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, the work required to pull the hanging part on the the table is
(a) $M g L$
(b) $\mathrm{Mgl} / 3$
(c) $\mathrm{Mg} \mathrm{L} / 9$
(d) $\mathrm{Mgl} / 18$

Narendra Kumar

Numerade Educator

Problem 25

During inelastic collision between two bodies, which of the following quantities always remain conserved? [NCERT Exemplar]
(a) Total kinetic energy
(b) Total mechanical energy
(c) Total linear momentum
(d) Speed of each body

Dheeraj Sharma

Numerade Educator

Problem 26

A spring of spring constant $5 \times 10^{3} \mathrm{Nm}^{-1}$ 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
(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 27

A rod $A B$ of mass $10 \mathrm{~kg}$ and length $4 \mathrm{~m}$ rests on a horizontal floor with end $A$ fixed so as to rotate it in vertical. Work done on the rod is $100 \mathrm{~J} .$ The height to which the end $B$ be raised vertically above the floor is
(a) $1.5 \mathrm{~m}$
(b) $2.0 \mathrm{~m}$
(c) $1.0 \mathrm{~m}$
(d) $2.5 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 28

Two inclined frictionless tracks, one gradual and the other steep meet at $A$ from where two stones are allowed to slide down from rest, one on each track as shown in figure.
Which of the following statement is correct? [NCERT Exemplar]
(a) Both the stones reach the bottom at the same time but not with the same speed
(b) Both the stones reach the bottom with the same speed and stone 1 reaches the bottom earlier than stone II
(c) Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone 1
(d) Both the stones reach the bottom at different times and with different speeds

Dheeraj Sharma

Numerade Educator

Problem 29

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) $\frac{2 A a^{5}}{3}$
(b) $\frac{2 A a^{5}}{3}+2 C a$
(c) $\frac{2 A a^{5}}{3}+\frac{B a^{2}}{2}+C a$
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 30

The relationship between force and position is shown in figure given (in one dimensional case). The work done by the force is displaying a body from $x=1 \mathrm{~cm}$ to $x=5 \mathrm{~cm}$ is
(a) $20 \mathrm{erg}$
(b) $60 \mathrm{erg}$
(c) 70 erg
(d) $700 \mathrm{erg}$

Dheeraj Sharma

Numerade Educator

Problem 31

A $10 \mathrm{~kg}$ brick moves along an $x$-axis. Its acceleration as a function of its position is shown in figure. What is the net work performed on the brick by the force causing the acceleration as the brick moves from $x=0$ to $x=8.0 \mathrm{~m}$ ?
(a) $4 \mathrm{~J}$
(b) $8 \mathrm{~J}$
(c) $2 \mathrm{~J}$
(d) $1 \mathrm{~J}$

Hunza Gilgit

Numerade Educator

Problem 32

A $2.0 \mathrm{~kg}$ block is dropped from a height of $40 \mathrm{~cm}$ onto a spring of spring constant $k=1960 \mathrm{Nm}^{-1}$, Find the maximum distance the spring is compressed.
(a) $0.080 \mathrm{~m}$
(b) $0.20 \mathrm{~m}$
(c) $0.40 \mathrm{~m}$
(d) $0.10 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 33

The graph between the resistive force $F$ acting on a body and the distance covered by the body is shown in the figure. The mass of the body is $2.5 \mathrm{~kg}$ and initial velocity is $2 \mathrm{~m} / \mathrm{s}$. When the distance covered by the body is $4 \mathrm{~m}$, its kinetic energy would be
(a) $50 \mathrm{~J}$
(b) $40 \mathrm{~J}$
(c) $20 \mathrm{~J}$
(d) $10 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 34

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 35

The potential energy function for a particle executing linear SHM is given by $V(x)=\frac{1}{2} k x^{2}$ where $k$ is the force constant of the oscillator. For $k=0.5 \mathrm{~N} / \mathrm{m}$, the graph of $V(x)$ versus $x$ is shown in the figure. A particle of total energy $E$ turns back when it reaches $x=\pm x_{m}$. If $V$ and $K$ indicate the $\mathrm{PE}$ and $\mathrm{KE}$ respectively of the particle at $x=\pm x_{m}$ then which of the following is correct? $\quad$ [NCERT Exemplar]
(a) $V=0, \bar{K}=\mathrm{E}$
(b) $V=\mathrm{E}, \bar{K}=0$
(c) $V<E, K=0$
(d) $V=0, K<0$

Dheeraj Sharma

Numerade Educator

Problem 36

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 in the 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) $\frac{1}{2} k y(2 x+y)$

Dheeraj Sharma

Numerade Educator

Problem 37

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of $60^{\circ}$ with the vertical with the same initial speed. At highest point of their journey, the ratio of their potential energies will be
(a) $1: 1$
(b) $2: 1$
(c) $3: 2$
(d) $4: 1$

Dheeraj Sharma

Numerade Educator

Problem 38

The kinetic energy $K$ of a particle moving in straight line depends upon the distance $s$ as
$$
K=a s^{2}
$$
The force acting on the particle is
(a) 2 as
(b) 2 mas
(c) $2 a$
(d) $\sqrt{a s^{2}}$

Dheeraj Sharma

Numerade Educator

Problem 39

A body of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $v=a x^{3 / 2}$ where $a=5 \mathrm{~m}^{-1 / 2} \mathrm{~s}^{-1}$. The work done by the net force during its displacement from $x=0$ to $x=2 \mathrm{~m}$ is $\quad$ [NCERT Exemplar]
(a) $1.5 \mathrm{~J}$
(b) $50 \mathrm{~J}$
(c) $10 \mathrm{j}$
(d) $100 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 40

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

Dheeraj Sharma

Numerade Educator

Problem 41

A $0.5 \mathrm{~kg}$ ball is thrown up with an initial speed $14 \mathrm{~m} / \mathrm{s}$ and reaches a maximum height of $8.0 \mathrm{~cm}$. How much energy is dissipated by air drag acting on the ball during the time of ascent?
(a) $19.6 \mathrm{~J}$
(b) $4.9 \mathrm{~J}$
(c) $10 \mathrm{~J}$
(d) $9.8 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 42

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shows the displacement-time curve for its motion? [NCERT Exemplar]

Dheeraj Sharma

Numerade Educator

Problem 43

A stone of mass $2 \mathrm{~kg}$ is projected upward with kinetic energy of $98 \mathrm{~J}$. The height at which the kinetic energy of the body becomes half its original value, is given by (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $5 \mathrm{~m}$
(b) $2.5 \mathrm{~m}$
(c) $1.5 \mathrm{~m}$
(d) $0.5 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 44

A ball whose kinetic energy is $E$, is projected at an angle $45^{\circ}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be
(a) $E$
(b) $\frac{E}{\sqrt{2}}$
(c) $\frac{E}{2}$
(d) zero

Dheeraj Sharma

Numerade Educator

Problem 45

A body is falling freely under the action of gravity alone in vacuum. Which of the following quantities remain constant during the fall? [NCERT Exemplar]
(a) Kinetic energy
(b) Potential energy
(c) Total mechanical energy
(d) Total linear energy

Dheeraj Sharma

Numerade Educator

Problem 46

The potential energy as a function of the force between two atoms in a diatomic molecules is given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^{6}}$, 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
(a) $x=\frac{a}{b}$
(b) $x=\sqrt{\frac{a}{b}}$
(c) $x=\frac{\sqrt{3 a}}{b}$
(d) $x=\sqrt[6]{\left(\frac{2 a}{b}\right)}$

Dheeraj Sharma

Numerade Educator

Problem 47

The potential energy of a particle of mass $5 \mathrm{~kg}$ moving in the $x y$-plane is given by $U=(-7 x+24 y) \mathrm{J}, x$ and $y$ being in metre. If the particle starts from rest from origin, then speed of particle at $t=2 \mathrm{~s}$ is
(a) $5 \mathrm{~ms}^{-1}$
(b) $01 \mathrm{~ms}^{-1}$
(c) $17.5 \mathrm{~ms}^{-1}$
(d) $10 \mathrm{~ms}^{-1}$

Dheeraj Sharma

Numerade Educator

Problem 48

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1 \mathrm{~m} / \mathrm{s}$, so as to have same kinetic energy as that of the boy. The original speed of the man will be
(a) $\sqrt{2} \mathrm{~m} / \mathrm{s}$
(b) $\sqrt{2-1} \mathrm{~m} / \mathrm{s}$
(c) $\frac{1}{\sqrt{2}-1} \mathrm{~m} / \mathrm{s}$
(d) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 49

If a body looses half of its velocity on penetrating $3 \mathrm{~cm}$ in a wooden block, then how much will it penetrate more before coming to rest?
(a) $1 \mathrm{~cm}$
(b) $2 \mathrm{~cm}$
(c) $3 \mathrm{~cm}$
(d) $4 \mathrm{~cm}$

Dheeraj Sharma

Numerade Educator

Problem 50

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 51

Two springs have force constants $k_{1}$ and $k_{2}$. These are extended through the same distance $x$. If their elastic energies are $E_{1}$ and $E_{2}$, then $\frac{E_{1}}{E_{2}}$ is equal to
(a) $k_{1}: k_{2}$
(b) $k_{2}: k_{1}$
(c) $\sqrt{k_{1}}: \sqrt{k_{2}}$
(d) $k_{1}^{2}: k_{2}^{2}$

Dheeraj Sharma

Numerade Educator

Problem 52

Which of the diagrams shown in figure represents variation of total mechanical energy of a pendulum oscillating in air as function of time? [NCERT Exemplar]

Dheeraj Sharma

Numerade Educator

Problem 53

A $50 \mathrm{~g}$ bullet moving with a velocity of $10 \mathrm{~ms}^{-1}$ gets embeded into a 950 g stationary body. The loss in kinetic energy of the system will be
(a) $95 \%$
(b) $100^{9}$
(c) $5 \%$
(d) $50 \%$

Dheeraj Sharma

Numerade Educator

Problem 54

A car is moving with a speed of $100 \mathrm{kmh}^{-1}$. If the mass of the car is $950 \mathrm{~kg}$, then its kinetic energy is
(a) $0.367 \mathrm{M}\rfloor$
(b) $3.67 \mathrm{~J}$
(c) $3.67 \mathrm{M} \mathrm{J}$
(d) $367 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 55

A simple pendulum is released from $A$ as shown. If $M$ and represent the mass of the bob and length of the pendulum respectively, the gain in kinetic energy at $B$ is
(a) $\frac{\mathrm{Mgl}}{2}$
(b) $\frac{\sqrt{3}}{2} \mathrm{Mgl}$
(c) $\frac{\mathrm{Mgl}}{\sqrt{2}}$
(d) $\frac{2}{\sqrt{3}} m g l$

Dheeraj Sharma

Numerade Educator

Problem 56

Two masses of $1 \mathrm{~g}$ and $4 \mathrm{~g}$ are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is
(a) $4: 1$
(b) $\sqrt{2}: 1$
(c) $1: 2$
(d) $1: 16$

Dheeraj Sharma

Numerade Educator

Problem 57

A mass of $5 \mathrm{~kg}$ is moving along a circular path of radius $1 \mathrm{~m}$. If the mass moves with 300 revolutions per minute, its kinetic energy would be [NCERT Exemplar]
(a) $250 \pi^{2}$
(b) $100 \pi^{2}$
(c) $5 \pi^{2}$
(d) 0

Dheeraj Sharma

Numerade Educator

Problem 58

A body of mass $2 \mathrm{~kg}$ is thrown up vertically with kinetic energy of $490 \mathrm{~J}$. The height at which the kinetic energy of the body becomes half of its original value is
(a) $50 \mathrm{~m}$
(b) $12.25 \mathrm{~m}$
(c) $25 \mathrm{~m}$
(d) $10 \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 59

In a shotput event an athlete throws the shotput of mass $10 \mathrm{~kg}$ with an inital speed of $1 \mathrm{~m} \mathrm{~s}^{-1}$ at $45^{\circ}$ from a height $1.5 \mathrm{~m}$ above ground. Assuming air resistance to be negligible and acceleration due to gravity to be $10 \mathrm{~ms}^{-2}$, the kinetic energy of the shotput when it just reaches the ground will be [NCERT Exemplar]
(a) $2.5 \mathrm{~J}$
(b) $5.0 \mathrm{~J}$
(c) $52.5 \mathrm{~J}$
(d) $155.0 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 60

A machine which is $75 \%$ efficient uses $12 \mathrm{~J}$ of energy in lifting up a $1 \mathrm{~kg}$ mass through a certain distance. The mass is then allowed to fall through that distance. The velocity of the ball at the end of its fall is
(a) $\sqrt{24} \mathrm{~ms}^{-1}$
(b) $\sqrt{32} \mathrm{~ms}^{-1}$
(c) $\sqrt{18} \mathrm{~ms}^{-1}$
(d) $3 \mathrm{~ms}^{-1}$

Dheeraj Sharma

Numerade Educator

Problem 61

A body of mass $4 \mathrm{~kg}$ is moving with momentum of $8 \mathrm{~kg}-\mathrm{ms}^{-1}$. A force of $0.2 \mathrm{~N}$ acts on it in the direction of motion of the body for 10 s. The increase in kinetic energy in joule is
(a) 10
(b) $8.5$
(c) $4.5$
(d) 4

Dheeraj Sharma

Numerade Educator

Problem 62

A body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x \mathrm{~cm}$ 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 63

A mass of $50 \mathrm{~kg}$ is raised through a certain height by a machine whose efficiency is $90 \%$, the energy is $5000 \mathrm{~J}$. If the mass is now released, its kinetic energy on hitting the ground shall be
(a) $5000 \mathrm{~J}$
(b) $4500 \mathrm{~J}$
(c) $4000 \mathrm{~J}$
(d) $5500 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 64

Given that the position of the body in metre is a function of time as follows
$$
x=2 t^{4}+5 t+4
$$
The mass of the body is $2 \mathrm{~kg}$. What is the increase in its kinetic energy, one second after the start of motion?
(a) $168 \mathrm{~J}$
(b) $169 \mathrm{~J}$
(c) 32$\rfloor$
(d) $144 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 65

A bomb of mass $3.0 \mathrm{~kg}$ explodes in air into two pieces of mass $2.0 \mathrm{~kg}$ and $1.0 \mathrm{~kg}$. The smaller mass goes at a speed of $80 \mathrm{~m} / \mathrm{s}$. The total energy imparted to the two fragment is
(a) $1.07 \mathrm{~kJ}$
(b) $2.14 \mathrm{~kJ}$
(c) $2.4 \mathrm{~kJ}$
(d) $4.8 \mathrm{~kJ}$

Dheeraj Sharma

Numerade Educator

Problem 66

A bomb of mass $9 \mathrm{~kg}$ explodes into 2 pieces of mass $3 \mathrm{~kg}$ and $6 \mathrm{~kg}$. The velocity of mass $3 \mathrm{~kg}$ is $1.6 \mathrm{~m} / \mathrm{s}$, the kinetic energy of mass $6 \mathrm{~kg}$ is
(a) $3.84 \mathrm{~J}$
(b) $9.6 \mathrm{~J}$
(c) $1.92 \mathrm{~J}$
(d) $2.92 \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 67

An engine pumps water continuously through a hole. Speed with which water passes through the hole nozzle is $v$ and $k$ is the mass per unit length of the water jet as it leaves the nozzle. Find the rate at which kinetic energy is being imparted to the water.
(a) $\frac{1}{2} k v^{2}$
(b) $\frac{1}{2} k v^{3}$
(c) $\frac{v^{2}}{2 k}$
(d) $\frac{v^{3}}{2 k}$

Dheeraj Sharma

Numerade Educator

Problem 68

In the stable equilibrium position, a body has
(a) maximum potential energy
(b) minimum potential energy
(c) minimum kinetic energy
(d) maximum kinetic energy

Dheeraj Sharma

Numerade Educator

Problem 69

A stone is dropped from the top of a tall tower. The ratio of the kinetic energy of the stone at the end of three seconds to the increase in the kinetic energy of the stone during the next three seconds is
(a) $1: 1$
(b) $1: 2$
(c) $1: 3$
(d) $1: 9$

Dheeraj Sharma

Numerade Educator

Problem 70

A rectangular plank of mass $m_{1}$ and height $a$ is kept on a horizontal surface. Another rectangular plank of mass $m_{2}$ and height $b$ is placed over the first plank. The gravitational potential energy of the system is
(a) $\left[m_{1}+m_{2}(a+b)\right] g$
(b) $\left[\left(\frac{m_{1}+m_{2}}{2} a+m_{2} \frac{b}{2}\right)\right] g$
(c) $\left[\left(\frac{m_{1}}{2}+m_{2}\right) a+m_{2} \frac{b}{2}\right] g$
(d) $\left[\left(\frac{m_{1}}{2}+m_{2}\right) a+m_{1} \frac{b}{2}\right] g$

Dheeraj Sharma

Numerade Educator

Problem 71

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to [NCERT]
(a) $t^{12}$
(b) $t$
(c) $t^{3 / 2}$
(d) $t^{2}$

Dheeraj Sharma

Numerade Educator

Problem 72

A $10 \mathrm{~m}$ long iron chain of linear mass density $0.8 \mathrm{~kg} \mathrm{~m}^{-1}$ is hanging freely from a rigid support. If $g=10 \mathrm{~ms}^{-2}$, then the power required to lift the chain upto the point of support in $10 \mathrm{~s}$ is
(a) $10 \mathrm{~W}$
(b) $20 \mathrm{~W}$
(c) $30 \mathrm{~W}$
(d) $40 \mathrm{~W}$

Dheeraj Sharma

Numerade Educator

Problem 73

A 10 HP motor pump out water from a well of depth $20 \mathrm{~m}$ and falls a water tank of volume 22380 litre at a height of $10 \mathrm{~m}$ from the ground the running time of the motor to fill the empty water tank is $\left(g=10 \mathrm{~ms}^{-2}\right.$ )
(a) $5 \mathrm{~min}$
(b) $10 \mathrm{~min}$
(c) $15 \mathrm{~min}$
(d) $20 \mathrm{~min}$

Dheeraj Sharma

Numerade Educator

Problem 74

An engine of power $7500 \mathrm{~W}$ makes a train move on a horizontal surface with constant velocity of $20 \mathrm{~ms}^{-1} .$ The force involved in the problem is
(a) $375 \mathrm{~N}$
(b) $400 \mathrm{~N}$
(c) $500 \mathrm{~N}$
(d) $600 \mathrm{~N}$

Dheeraj Sharma

Numerade Educator

Problem 75

A one kilowatt motor is used to pump water from a well $10 \mathrm{~m}$ deep. The quantity of water pumped out per second is nearly
(a) $1 \mathrm{~kg}$
(b) $10 \mathrm{~kg}$
(c) $100 \mathrm{~kg}$
(d) $1000 \mathrm{~kg}$

Dheeraj Sharma

Numerade Educator

Problem 76

A car manufacturer claims that his car can be 82 accelerated from rest to a velocity of $10 \mathrm{~ms}^{-1}$ in $5 \mathrm{~s}$. If the total mass of the car and its occupants is $1000 \mathrm{~kg}$, then the average horse power developed by the engine is
(a) $\frac{10^{3}}{746}$
(b) $\frac{10^{4}}{746}$
(d) 8

Dheeraj Sharma

Numerade Educator

Problem 77

Which of the diagrams in figure correctly shows the change in kinetic energy of an iron sphere falling freely in a lake having sufficient depth to impart it a terminal velocity? [NCERT Exemplar]

Dheeraj Sharma

Numerade Educator

Problem 78

A dam is situated at a height of $550 \mathrm{~m}$ above sea level and supplies water to a power house which is at a height of $50 \mathrm{~m}$ above sea level. $2000 \mathrm{~kg}$ of water passes through the turbines per second. What would be the maximum electrical power output of the power house if the whole system were $80 \%$ efficient?
(a) $8 \mathrm{MW}$
(b) $10 \mathrm{MW}$
(c) $12.5 \mathrm{MW}$
(d) $16 \mathrm{MW}$

Dheeraj Sharma

Numerade Educator

Problem 79

An automobile weighing $1200 \mathrm{~kg}$ climbs up a hill that rises $1 \mathrm{~m}$ in 20 s. Neglecting frictional effects, the minimum power developed by the engine is $9000 \mathrm{~W}$. If $g=10 \mathrm{~ms}^{-2}$, then the velocity of the automobile is
(a) $36 \mathrm{kmh}^{-1}$
(b) $54 \mathrm{kmh}^{-1}$
(c) $72 \mathrm{kmh}^{-1}$
(d) $90 \mathrm{kmh}^{-1}$

Subash Charan

Numerade Educator

Problem 80

A $500 \mathrm{~kg}$ car, moving with a velocity of $36 \mathrm{kmh}^{-1}$ on a straight road unidirectionally, doubles its velocity in one minute. The power delivered by the engine for doubling the velocity is
(a) $750 \mathrm{~W}$
(b) $1050 \mathrm{~W}$
(c) $1150 \mathrm{~W}$
(d) $1250 \mathrm{~W}$

Dheeraj Sharma

Numerade Educator

Problem 81

The power of a water jet flowing through an orifice of radius $r$ with velocity $v$ is
(a) zero
(b) $500 \pi r^{2} v^{2}$
(c) $500 \pi r^{2} v^{3}$
(d) $\pi r^{4} v$

Subash Charan

Numerade Educator

Problem 82

A motor of power $P_{0}$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times. The power of the motor is increassed to $p_{1}$. The ratio of $p_{1}$ to $p_{0}$ is
(a) $n: 1$
(b) $n^{2}: 1$
(c) $n^{3}: 1$
(d) $n^{4}: 1$

Subash Charan

Numerade Educator

Problem 83

A quarter horse power motor runs at a speed of $600 \mathrm{rpm}$. Assuming $40 \%$ efficiency, the work done by the motor in one rotation will be
(a) 7.46]
(b) $7400 \mathrm{~J}$
(c) $7.46 \mathrm{erg}$
(d) $74.6 \mathrm{~J}$

Subash Charan

Numerade Educator

Problem 84

Ten litre of water per second is lifted from well through $20 \mathrm{~m}$ and delivered with a velocity of $10 \mathrm{~ms}^{-1}$, then the power of the motor is
(a) $1.5 \mathrm{~kW}$
(b) $2.5 \mathrm{~kW}$
(c) $3.5 \mathrm{~kW}$
(d) $4.5 \mathrm{~kW}$

Subash Charan

Numerade Educator

Problem 85

A body is moved along a straight line by 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 86

One man takes 1 minute to raise a box to a height of $1 \mathrm{~m}$ and another man takes $\frac{1}{2}$ minute to do so. The energy of the two is
(a) different
(b) same
(c) energy of the first is more
(d) energy of the second is more

Dheeraj Sharma

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) $x^{1 / 2}$
(b) $x$
(c) $x^{2}$
(d) $x^{1 / 3}$

Hunza Gilgit

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 $a_{e}=k^{2} r t^{2}$. 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

Hunza Gilgit

Numerade Educator