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Objective Physics : NEET 2020 Examination textbook Gurukul Oswal

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Chapter 4

WORK, ENERGY AND POWER - all with Video Answers

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Section 1

Work, Energy, and Power

01:22

Problem 1

A uniform force of $(3 \hat{i}+\hat{j})$ newton acts on a particle of mass $2 \mathrm{~kg}$. Hence the particle is displaced from position $(2 \hat{i}+\hat{k}) \mathrm{m}$ to position $(4 \hat{i}+3 \hat{j}-\hat{k}) \mathrm{m}$. The
work done by the force on the particle is:
(a) $9 \mathrm{~J}$
(b) $6 \mathrm{~J}$
(c) $13 \mathrm{~J}$
(d) $15 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
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01:52

Problem 2

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \mathrm{~kg}$ moves with a speed of $12 \mathrm{~m} \mathrm{~s}^{-1}$ and the second part of mass $2 \mathrm{~kg}$ moves with $8 \mathrm{~m} \mathrm{~s}^{-1}$ speed. If the third part flies off with $4 \mathrm{~m} \mathrm{~s}^{-1}$ speed, then its mass is:
(a) $3 \mathrm{~kg}$
(b) $5 \mathrm{~kg}$
(c) $7 \mathrm{~kg}$
(d) $17 \mathrm{~kg}$

Dheeraj Sharma
Dheeraj Sharma
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02:37

Problem 3

A body is being raised to a height $h$ from the surface of Earth. What is the sign of work done by applied force and gravitational force respectively?
(a) Positive, Positive
(b) Positive, Negative
(c) Negative, Positive
(d) Negative, Negative

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:31

Problem 4

Which of the following is not a conservative force?
(a) Elastic force
(b) Gravitational force
(c) Force of friction
(d) Electrostatic force

Dheeraj Sharma
Dheeraj Sharma
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02:33

Problem 5

A weight lifter lifts a $275 \mathrm{~kg}$ barbell from the ground to a height of $2.4 \mathrm{~m}$. How much work has he done in lifting the barbell, and how much work is required to hold the weight at that height?

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:18

Problem 6

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 $4 \mathrm{~kg}$. The work done in pulling the entire chain on the table (Take $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$ ).
(a) $12.9 \mathrm{~J}$
(b) $6.3 \mathrm{~J}$
(c) $7.2 \mathrm{~J}$
(d) $2.0 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
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01:36

Problem 7

A body of mass $2 \mathrm{~kg}$ moving under a force has relation between displacement $x$ and time $t$ as $x=t^{3} / 3$ where $x$ is in the metre and $t$ is in the second. The work done by the body in first two second will be:
(a) $1.6$ Joule
(b) 16 Joule
(c) 160 Joule
(d) 1,600 Joule

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:24

Problem 8

A body of mass $1 \mathrm{~kg}$ begins to move under the action of a time dependent force $F=\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{N}$, where $i$ and $\breve{j}$ are unit vectors along $x$ -axis and $y$ -axis. What power will be developed by the force at the time $t$ ?
(a) $\left(2 t^{2}+3 t^{3}\right) \mathrm{W}$
(b) $\left(2 t^{2}+4 t^{4}\right) \mathrm{W}$
(c) $\left(2 t^{3}+3 t^{4}\right) \mathrm{W}$
(d) $\left(2 t^{3}+3 t^{5}\right) \mathrm{W}$

Dheeraj Sharma
Dheeraj Sharma
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01:13

Problem 9

A body is acted upon a force $\vec{F}=-i+2 j+3 k$. The work done by the force in displaying it for $(0,0,0)$ to $(0,0,4 \mathrm{~m})$ will be:
(a) $12 \mathrm{~J}$
(b) $10 \mathrm{~J}$
(c) $8 \mathrm{~J}$
(d) $6 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:40

Problem 10

The work done in pulling a body of mass $5 \mathrm{~kg}$ along an inclined plane (angle $60^{\circ}$ ) with coefficient of friction $0.2$ through $2 \mathrm{~m}$, will be:
(a) $94.66 \mathrm{~J}$
(b) $94.08 \mathrm{~J}$
(c) $90.08 \mathrm{~J}$
(d) $91.08 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:34

Problem 11

A force $\mathrm{F}=\left(7-2 x+3 x^{2}\right) \mathrm{N}$ applied on a $2 \mathrm{~kg}$ mass which displaces it from $x=0$ to $x=5 \mathrm{~m}$. Work done in joule is:
(a) $70 \mathrm{~J}$
(b) $270 \mathrm{~J}$
(c) $35 \mathrm{~J}$
(d) $135 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:42

Problem 12

Two similar springs $\mathrm{P}$ and $\mathrm{Q}$ have spring constants $\mathrm{k}_{\mathrm{p}}$ and $\mathrm{k}_{\mathrm{Q}}$, such that $\mathrm{k}_{\mathrm{p}}>\mathrm{k}_{\mathrm{Q}}$. They are stretched, first
by the same amount (case $\mathrm{a}_{3}$ ) then by the same force (case b). The work done by the springs $\mathrm{W}_{\mathrm{p}}$ and $\mathrm{W}_{\mathrm{Q}}$ are related as, in case (a) and case (b), respectively:
(a) $W_{\mathrm{p}}=W_{\mathrm{Q}} ; W_{\mathrm{p}}=W_{\mathrm{Q}}$
(b) $W_{\mathrm{p}}>W_{\mathrm{Q}} ; W_{\mathrm{Q}}>W_{\mathrm{p}}$
(c) $W_{\mathrm{p}}<W_{\mathrm{Q}} ; W_{\mathrm{Q}}<W_{\mathrm{P}}$
(d) $W_{\mathrm{p}}=W_{Q} ; W_{\mathrm{p}}>W_{\mathrm{Q}}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:19

Problem 13

A cord is used to lower vertically a block of mass $M$, a distance $\mathrm{d}$ at a constant downward acceleration of $\mathrm{g} / 4 .$ The work done by the cord on the block is:
(a) $M g d / 4$
(b) $3 \mathrm{Mg} d / 4$
(c) $-3 M \mathrm{~g} d / 4$
(d) $M \mathrm{~g} d$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:43

Problem 14

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:
(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
Dheeraj Sharma
Numerade Educator
03:13

Problem 15

A particle of mass $10 \mathrm{~g}$ moves along a circle of radius $6.4 \mathrm{~cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4} \mathrm{~J}$ by the end of the second revolution after the beginning of the motion?
(a) $0.1 \mathrm{~m} / \mathrm{s}^{2}$
(b) $0.15 \mathrm{~m} / \mathrm{s}^{2}$
(c) $0.18 \mathrm{~m} / \mathrm{s}^{2}$
(d) $0.2 \mathrm{~m} / \mathrm{s}^{2}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:16

Problem 16

A peculiar spring has a force law $F=-\mathrm{d} x^{3}$ which of the following is true?
(a) Potential energy at point $x$ when $U=0$ at $x=0$ $\frac{\mathrm{d} x^{4}}{4}$
(b) If a mass $\mathrm{m}$ is attached to the spring. Mass is displaced slightly, it will follow simple harmonic motion.
(c) $\frac{\mathrm{d} x^{4}}{4}$ work has to be done on the spring $\mathrm{i}_{n}$ stretching it slowing from 0 to $x$.
(d) None of these

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:21

Problem 17

A spring of force constant $800 \mathrm{~N} / \mathrm{m}$ has an extension of $5 \mathrm{~cm}$. The work done in extending it from $5 \mathrm{~cm}$ to $15 \mathrm{~cm}$ is:
(a) $6 \mathrm{~J}$
(b) $8 \mathrm{~J}$
(c) $32 \mathrm{~J}$
(d) $24 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:45

Problem 18

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:
(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
Dheeraj Sharma
Numerade Educator
01:52

Problem 19

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
Dheeraj Sharma
Numerade Educator
02:31

Problem 20

A uniform thread of length $2 \mathrm{~m}$ is lying on a stool such that a length of $60 \mathrm{~cm}$ hangs freely from the edge of the stool. The total mass of the thread is $4 \mathrm{~kg}$. What is the work done in pulling the entire thread on the stool?
(a) $7.2 \mathrm{~J}$
(b) $3.6 \mathrm{~J}$
(c) $120 \mathrm{~J}$
(d) $1200 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:34

Problem 21

A block of mass $10 \mathrm{~kg}$ is moving in $x$ -direction with a constant speed of $10 \mathrm{~m} \mathrm{~s}^{-1} .$ It is subjected to a retarding force $F_{r}=-0.1 \mathrm{~J} \mathrm{~m}^{-1}$ during its travel from $x=20 \mathrm{~m}$ to $x=30 \mathrm{~m}$. Its final kinetic energy will be:
(a) $250 \mathrm{~J}$
(b) $275 \mathrm{~J}$
(c) $450 \mathrm{~J}$
(d) $475 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:52

Problem 22

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
Mahendra K
Numerade Educator
01:18

Problem 23

If the water falls from a dam into a turbine wheel $19.6 \mathrm{~m}$ below, then the velocity of water at the turbine is: $(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s})$
(a) $9.8 \mathrm{~m} / \mathrm{s}$
(b) $19.6 \mathrm{~m} / \mathrm{s}$
(c) $39.2 \mathrm{~m} / \mathrm{s}$
(d) $98 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:38

Problem 24

A bullet fired from a gun can pierce a target due to its:
(a) Mechanical energy
(b) Heat energy
(c) Kinetic energy
(d) Acceleration

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:57

Problem 25

When force and displacement are in the same direction, the kinetic energy of the body:
(a) Increases
(b) Decreases
(c) Remains constant
(d) Becomes zero

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:09

Problem 26

The momentum of a body of mass $5 \mathrm{~kg}$ is $500 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$. Find its kinetic energy.
(a) $2 \times 10^{5} \mathrm{~J}$
(b) $2.5 \times 10^{4} \mathrm{~J}$
(c) $2.5 \times 10^{5} \mathrm{~J}$
(d) $2.5 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:02

Problem 27

A bullet of mass $20 \mathrm{~g}$ is found to pass two points $30 \mathrm{~m}$ apart in a time interval of $4 \mathrm{~s}$. Calculate the kinetic energy of the bullet if it moves with constant speed.
(a) $2.5 \mathrm{~J}$
(b) $5 \mathrm{~J}$
(c) $0.5625 \mathrm{~J}$
(d) $2 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:43

Problem 28

The kinetic energy in water is used to
(a) run turbines.
(b) generate nuclear power.
(c) generate hydroelectricity.
(d) thermal power.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:26

Problem 29

What energy does a stretched bow possess?
(a) Kinetic energy
(b) Gravitational energy
(c) Elastic potential energy
(d) Potential energy

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:50

Problem 30

A ball whose kinetic energy is $E$, is projected at an angle of $45^{\circ}$ 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
Dheeraj Sharma
Numerade Educator
02:03

Problem 31

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:
(a) $x^{2}$
(b) $\mathrm{e}^{\mathrm{x}}$
(c) $x$
(d) $\log _{e} x$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:03

Problem 32

The blades of a windmill sweep out a circle of area $A$. If the wind flows at a velocity $v$ perpendicular to the circle, what is the kinetic energy of mass of the air of density $\rho$ passing through it in time $t$ ?
(a) $A v \rho t$
(b) $2 A v \rho t$
(c) $A v^{2} \rho t$
(d) $\frac{1}{2} A v^{3} \rho t$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:59

Problem 33

In the question number 32, Assume that the windmill converts $25 \%$ of the wind's energy into electrical energy, and that $A=30 \mathrm{~m}^{2}, v=36 \mathrm{~km} / \mathrm{h}$ and the density of air is $1.2 \mathrm{~kg} \mathrm{~m}^{-3}$. What is the electrical power produced?
(a) $3.25 \mathrm{~kW}$
(b) $12.5 \mathrm{~kW}$
(c) $4.5 \mathrm{~kW}$
(d) $11.0 \mathrm{~kW}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:55

Problem 34

A particle of mass $m_{1}$ is moving with a velocity $v_{1}$ and another particle of mass $m_{2}$ is moving with a velocity $v_{2} .$ Both have the same momentum, but their different kinetic energies are $E_{1}$ and $E_{2}$ respectively. If $m_{1}>m_{2}$ then:
(a) $E_{1}=E_{2}$
(b) $E_{1}<E_{2}$
(c) $\frac{E_{1}}{E_{2}}=\frac{m_{1}}{m_{2}}$
(d) $E_{1}>E_{2}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:14

Problem 35

A body of mass $m$ is dropped from a certain height. It has velocity $v_{1}$ when it is at a height $h_{1}$ above the ground. It has velocity $v_{2}$ when it is at a height $h_{2}$ above the ground which of the following is true:
(a) $v_{1}^{2}-v_{2}^{2}=2 g\left(h_{1}-h_{2}\right)$
(b) $v_{1}^{2}-v_{2}^{2}=2 g\left(h_{2}-h_{1}\right)$
(c) $v_{1}-v_{2}=\sqrt{2 g}\left(\sqrt{h_{2}}-\sqrt{h}_{1}\right)$
(d) $v_{1}-v_{2}=\sqrt{2 g}\left(\sqrt{h_{1}}-\sqrt{h_{2}}\right)$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:54

Problem 36

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:
(a) $\frac{3}{\sqrt{2}}$
(b) $\sqrt{2}$
(c) $\frac{1}{\sqrt{2}}$
(d) 2

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:23

Problem 37

Two springs of force constants $300 \mathrm{~N} / \mathrm{m}$ (Spring $\mathrm{A}$ ) and $400 \mathrm{~N} / \mathrm{m}$ (Spring B) are joined together in series. The combination is compressed by $8.75 \mathrm{~cm}$. The ratio of energy stored in $\mathrm{A}$ and $\mathrm{B}$ is $E_{A} / E_{B}$. Then $E_{A} / E_{B}$ is equal to:
(a) $4 / 3$
(b) $16 / 9$
(c) $3 / 4$
(d) $9 / 16$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:21

Problem 38

The potential energy of a certain spring when stretched through distance $S$ is 10 joules. The amount of work done (in joule) that must be done on this spring to stretch it through an additional distance $S$, will be:
(a) 20
(b) 10
(c) 30
(d) 40

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:22

Problem 39

Potential energy is also called as
(a) gravitational energy.
(b) mutual energy.
(c) kinetic energy.
(d) average energy.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:30

Problem 40

The total energy of the universe is
(a) constant.
(b) variable.
(c) infinity.
(d) continuity.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:19

Problem 41

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 done to a horizontal base at a height of $20 \mathrm{~m}$ above the ground. The velocity attained by the ball is:
(a) $10 \mathrm{~m} / \mathrm{s}$
(b) $10 \sqrt{30 \mathrm{~m} / \mathrm{s}}$
(c) $40 \mathrm{~m} / \mathrm{s}$
(d) $20 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:23

Problem 42

The KE acquired by a mass $m$ in travelling a certain distance $d$, starting form rest, under the action of a constant force is directly proportional to:
(a) $m$
(b) $\sqrt{m}$
(c) $\frac{1}{\sqrt{m}}$
(d) independent of $m$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:24

Problem 43

A spring lies along an $x$ -axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at $x=0 .$ A force of constant magnitude $F$ is applied to the block that begins to compress the spring, until the block comes to a maximum displacement $x_{\max ^{*}}$
During the displacement, which of the curves shown in the graph best represents the kinetic energy of the block?
(a) 1
(b) 2
(c) 3
(d) 4

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:01

Problem 44

Identify the false statement from the following
(a) Work-energy theorem is not independent of Newton's second law.
(b) Work-energy theorem holds in all inertial frames.
(c) Work done by friction over a closed path is zero.
(d) No potential energy can be associated with friction.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:35

Problem 45

The relationship between the force $F$ and position $x$ of a body is as shown in figure. The work done in displacing the body for $x=1 \mathrm{~m}$ to $x=5 \mathrm{~m}$ will be:
(a) $30 \mathrm{~J}$
(b) $15 \mathrm{~J}$
(c) $25 \mathrm{~J}$
(d) $20 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:45

Problem 46

An object of mass $5 \mathrm{~kg}$ falls from rest through a vertical distance of $20 \mathrm{~m}$ and reaches a velocity of $10 \mathrm{~m} / \mathrm{s}$. How much work is done by the push of the air on the object? Taken: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{-2}\right)$
(a) $350 \mathrm{~J}$
(b) $-750 \mathrm{~J}$
(c) $200 \mathrm{~J}$
(d) $300 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:08

Problem 47

A gardener pushes a lawn roller through $20 \mathrm{~m}$. If he applies a force of $20 \mathrm{~kg}$ weight in a direction inclined at $60^{\circ}$ to the ground, find the work done by him. $\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $400 \mathrm{~J}$
(b) $1960 \mathrm{~J}$
(c) $250 \mathrm{~J}$
(d) $2514 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:45

Problem 48

A person is holding a bucket by applying a force of 10
N. He moves a horizontal distance of $5 \mathrm{~m}$ and then climbs up a vertical distance of $10 \mathrm{~m}$. Find the total work done by him.
(a) $50 \mathrm{~J}$
(b) $150 \mathrm{~J}$
(c) $100 \mathrm{~J}$
(d) $200 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:06

Problem 49

If a force acts perpendicular to the direction of motion of a body, what is the amount of work done?
(a) Infinity
(b) Constant
(c) Zero
(d) $\sin \theta$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:44

Problem 50

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

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:59

Problem 51

When a body falls freely under gravity, then the work done by the gravity is:
(a) Positive
(b) Negative
(c) Zero
(d) Infinity

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:44

Problem 52

When a body slides against a rough horizontal surface, the work done by friction is:
(a) Positive
(b) Zero
(c) Negative
(d) Constant

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:45

Problem 53

For a body moving in a circular path, the work done by the centripetal force is:
(a) Negative
(b) Positive
(c) Constant
(d) Zero

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:16

Problem 54

Raindrop of mass 1 g falling from a height of $1 \mathrm{~km}$ hits the ground with a speed of $50 \mathrm{~m} \mathrm{~s}^{-1}$. If the resistive force is proportional to the speed of the drop, then the work done by the resistive force is:
(a) $10 \mathrm{~J}$
(b) $-10 \mathrm{~J}$
(c) $8.75 \mathrm{~J}$
(d) $-8.75 \mathrm{~J}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:13

Problem 55

Two bodies of mass $m$ and $4 m$ have equal kinetic energy. What is the ratio of their momentum?
(a) $1: 4$
(b) $1: 2$
(c) $\overline{1: 1}$
(d) $2: 1$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:00

Problem 56

An object of mass $m$ is released from rest from the top of a smooth inclined plane of height $h$. Its speed at the bottom of the plane is proportional to:
(a) $\mathrm{m}^{-1}$
(b) $\mathrm{m}$
(c) $\mathrm{m}^{2}$
(d) None of these

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:58

Problem 57

The kinetic energy of a particle moving along a circle of radius $\mathrm{R}$ depend on the distance covered $S$ as $\mathrm{T}=\mathrm{a} S^{2}$ where a is constant. Find the force acting on the particle as a function of $S:$
(a) $\frac{2 \mathrm{a} S^{2}}{R}$
(b) $2 a S \sqrt{1+\left(\frac{S}{R}\right)^{2}}$
(d) None of these

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:03

Problem 58

A body is allowed to fall freely under gravity from height of $10 \mathrm{~m}$. If it loses $25 \%$ of its energy due to impact with the ground, then the maximum height it rises after one impact is:
(a) $5.5 \mathrm{~m}$
(b) $5.0 \mathrm{~m}$
(c) $7.5 \mathrm{~m}$
(d) $8.2 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:15

Problem 59

A small object of mass $m=234 \mathrm{~g}$ slides along a track with elevated ends and a central flat part, as shown in below figure. The flat part has a length $L=2.16 \mathrm{~m}$. The curved portions the tracks are frictionless; but in traversing the flat part, the object loses $688 \mathrm{~mJ}$ of mechanical energy, due to friction. The object is released at point $\mathrm{A}$, which is a height $h=1.05 \mathrm{~m}$ above the flat part of the track. Where does the object finally come to rest?
(a) $3.50$
(b) $5.00$
(c) $8.70$
(d) $2.50$

Ajay Singhal
Ajay Singhal
Numerade Educator
01:49

Problem 60

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:
(a) 2
(b) $\frac{3}{\sqrt{2}}$
(d) $\frac{1}{\sqrt{2}}$
(c) $\sqrt{2}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:00

Problem 61

A simple pendulum consists of a mass attached to a light string $l .$ if the system is oscillating through small angles which of the following is true?
(a) The frequency is independent of the acceleration due to gravity $\mathrm{g}$.
(b) The period depends on the amplitude of the oscillation.
(c) The period is independent of mass $m$.
(d) The period is independent of length $l$.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:49

Problem 62

A boy is swinging on a swing such that his lowest and highest positions are at heights $2 \mathrm{~m}$ and $4.5 \mathrm{~m}$ respectively. His velocity at lowest position is:
(a) $5 \sqrt{2} \mathrm{~m} / \mathrm{s}$
(b) $2 \sqrt{5} \mathrm{~m} / \mathrm{s}$
(c) $2 \sqrt{3} \mathrm{~m} / \mathrm{s}$
(d) $7 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:23

Problem 63

A ball is falling from a height of $2 \mathrm{~m}$ rebounds to a height of $1.5 \mathrm{~m}$ after hitting the ground. Then the percentage of energy lost is:
(a) $25 \%$
(b) $30 \%$
(c) $50 \%$
(d) $100 \%$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:43

Problem 64

A spring gun of spring constant $90 \mathrm{~N} \mathrm{~cm}^{-1}$ is compressed $12 \mathrm{~cm}$ by a ball of mass $16 \mathrm{~g}$. If the trigger is pulled, Find the velocity of the ball.
(a) $50 \mathrm{~ms}^{-1}$
(b) $40 \mathrm{~ms}^{-1}$
(c) $60 \mathrm{~ms}^{-1}$
(d) $90 \mathrm{~ms}^{-1}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:34

Problem 65

Water drop of mass $1 \mathrm{~g}$ falling from a height of $1 \mathrm{~km}$ hits the ground with a speed of $50 \mathrm{~ms}^{-1}$. Which of the following statements is correct? (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) The loss of potential energy of the drop is $10 \mathrm{~J}$.
(b) The gain in kinetic energy of the drop is $1.25 \mathrm{~J}$.
(c) The gain in kinetic energy of the drop is not equal to the loss of potential energy of the drop.
(d) All of these

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:35

Problem 66

Calculate the velocity of the bob of a simple pendulum at its mean position if it can rise to a vertical height of $10 \mathrm{~cm}$. (Take $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$ )
(a) $5 \mathrm{~m} / \mathrm{s}$
(b) $1.5 \mathrm{~m} / \mathrm{s}$
(c) $14 \mathrm{~m} / \mathrm{s}$
(d) $1.4 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:03

Problem 67

How high must the body be lifted to gain an amount of potential energy equal to the kinetic energy it has when moving at a speed of $20 \mathrm{~m} / \mathrm{s} ?\left(\mathrm{~g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $20 \mathrm{~m}$
(b) $20.2 \mathrm{~m}$
(c) $20.0 \mathrm{~m}$
(d) $2.2 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:16

Problem 68

A ball is thrown vertically upwards with a velocity of $20 \mathrm{~m} / \mathrm{s}$. At what height, will its kinetic energy be half its original value?
(a) $10.20 \mathrm{~m}$
(b) $10 \mathrm{~m}$
(c) $15 \mathrm{~m}$
(d) $5 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:31

Problem 69

An automobile of mass $m$ accelerates from rest. If die engine supplies a constant power $P$, the velocity at time $t$ is given by:
(a) $v=\frac{P_{t}}{m}$
(b) $v=\frac{2 P_{t}}{m}$
(c) $v=\sqrt{\frac{P_{t}}{m}}$
(d) $v=\sqrt{\frac{2 P_{t}}{m}}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:35

Problem 70

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2 \mathrm{~m} / \mathrm{s}$. The mass per unit length of water in the pipe is $100 \mathrm{~kg} / \mathrm{m}$. What is the power of the engine?
(a) $400 \mathrm{~W}$
(b) $200 \mathrm{~W}$
(c) $100 \mathrm{~W}$
(d) $800 \mathrm{~W}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:09

Problem 71

A one-ton car moves with a constant velocity of $15 \mathrm{~ms}^{-1}$ on a rough horizontal road. The total resistance to the motion of the car is $12 \%$ of the weight of the car. The power required to keep the car moving with the same constant velocity of $15 \mathrm{~ms}^{-1}$ is: (Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
(a) $9 \mathrm{~kW}$
(b) $18 \mathrm{~kW}$
(c) $24 \mathrm{~kW}$
(d) $36 \mathrm{~kW}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:07

Problem 72

Water falls from a height of $60 \mathrm{~m}$ at the rate of $15 \mathrm{~kg} / \mathrm{s}$ to operate a turbine. The losses due to frictional force are $10 \%$ of energy. How much power is generated by the turbine? $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{-2}\right)$
(a) $8.1 \mathrm{~kW}$
(b) $10.2 \mathrm{KW}$
(c) $12.3 \mathrm{~kW}$
(d) $7.0 \mathrm{~kW}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:41

Problem 73

A force applied by an engine of a train of mass $2.05 \times 10^{6} \mathrm{~kg}$ changes its velocity from $5 \mathrm{~m} / \mathrm{s}$ to $25 \mathrm{~m} / \mathrm{s}$ in 5 minutes. The power of the engine is:
(a) $1.025 \mathrm{MW}$
(b) $2.05 \mathrm{MW}$
(c) $5 \mathrm{MW}$
(d) $6 \mathrm{MW}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:36

Problem 74

A particle of mass $m$ is driven by a machine that delivers a constant power of $k$ watts. If the particle starts from rest the force on the particle at time $t$ is:
(a) $\sqrt{m k t}^{-1 / 2}$
(b) $\sqrt{2 m k t}^{-1 / 2}$
(c) $\frac{1}{2} \sqrt{m k t}-{ }^{-1 / 2}$
(d) $\sqrt{\frac{m k}{2} t^{-1 / 2}}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:29

Problem 75

How much mass is converted into energy per day in Tarapur nuclear power plant operated at $10^{7} \mathrm{~kW}$ ?
(a) $10 \mathrm{~g}$
(b) $9 \mathrm{~g}$
(c) $9.6 \mathrm{~g}$
(d) $2 \mathrm{~g}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:08

Problem 76

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
Dheeraj Sharma
Numerade Educator
01:31

Problem 77

A machine gun fires 60 bullets per minute, with a velocity of $700 \mathrm{~m} / \mathrm{s}$. If each bullet has a mass of $50 \mathrm{~g}$, find the power developed by the gun.
(a) $1225 \mathrm{~W}$
(b) $12250 \mathrm{~W}$
(c) $122.5 \mathrm{~W}$
(d) $122 \mathrm{~W}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:29

Problem 78

A man weighing $60 \mathrm{~kg}$ climbs up a staircase carrying a load of $20 \mathrm{~kg}$ on his head. The stair case has 20 steps each of height $0.2 \mathrm{~m}$. If he takes $10 \mathrm{~s}$ to climb, find his power.
(a) $313.6 \mathrm{~W}$
(b) $120.6 \mathrm{~W}$
(c) $510 \mathrm{~W}$
(d) 0

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:02

Problem 79

A $30 \mathrm{~m}$ deep well is having water up to $15 \mathrm{~m}$. An engine evacuates it in one hour. The power of the engine, if the diameter of the well is $4 \mathrm{~m}$ is:
(a) $11.55 \mathrm{~kW}$
(b) $1155 \mathrm{~kW}$
(c) $23.10 \mathrm{~kW}$
(d) $2310 \mathrm{~kW}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:42

Problem 80

Two men with weights in the ratio $4: 3$ run up a staircase in time in the ratio $12: 11$. The ratio of power of the first to that of second is:
(a) $\frac{4}{3}$
(b) $\frac{12}{11}$
(c) $\frac{48}{33}$
(d) $\frac{11}{9}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:20

Problem 81

Water is flowing in a river at $2 \mathrm{~ms}^{-1}$. The river is $50 \mathrm{~m}$ wide and has an average depth of $5 \mathrm{~m}$. The power available from the current in the river is: (Density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )
(a) $0.5 \mathrm{MW}$
(c) $1.5 \mathrm{MW}$
(b) $1 \mathrm{MW}$
(d) $2 \mathrm{MW}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
04:57

Problem 82

A glass marble dropped from a certain height above the horizontal surface reaches the surface in time $t$ and then continues to bounce up and down. The time in which the marble finally comes to rest is:
(a) $e^{n} t$
(b) $e^{2} t$
(c) $t\left[\frac{1+e}{1-e}\right]$
(d) $t\left[\frac{1-e}{1+e}\right]$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:00

Problem 83

A bullet of mass $20 \mathrm{~g}$ and moving with $600 \mathrm{~m} / \mathrm{s}$ collides with a block of mass $4 \mathrm{~kg}$ hanging with the string. What is the velocity of bullet when it comes out of block, if block rises to height $0.2 \mathrm{~m}$ after collision?
(a) $200 \mathrm{~m} / \mathrm{s}$
(b) $150 \mathrm{~m} / \mathrm{s}$
(c) $400 \mathrm{~m} / \mathrm{s}$
(d) $300 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:41

Problem 84

A block $C$ of mass $m$ is moving with velocity $v_{0}$ and collides elastically with block A of mass $\mathrm{m}$ and connected to another block B of mass $2 \mathrm{~m}$ through spring constant $\mathrm{k}$. What is $\mathrm{k}$ if $x_{0}$ is compression of spring when velocity of $\mathrm{A}$ and $\mathrm{B}$ is same?
(a) $\frac{m v_{0}^{2}}{x_{0}^{2}}$
(b) $\frac{m v_{0}^{2}}{2 x_{0}^{2}}$
(c) $\frac{3}{2} \frac{m v_{0}^{2}}{x_{0}^{2}}$
(d) $\frac{2}{3} \frac{m v_{0}^{2}}{x_{0}^{2}}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:53

Problem 85

A ball is thrown vertically downwards from a height of $20 \mathrm{~m}$ with an initial velocity $v_{0}$. It collides with the ground and loses $50 \%$ of its energy in collision and rebounds to the same height. The initial velocity $v_{0}$ is:
(Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
(a) $20 \mathrm{~ms}^{-1}$
(b) $28 \mathrm{~ms}^{-1}$
(c) $10 \mathrm{~ms}^{-1}$
(d) $14 \mathrm{~ms}^{-1}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:51

Problem 86

Consider a rubber ball freely falling from a height $h$ $=4.9 \mathrm{~m}$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as:

Ajay Singhal
Ajay Singhal
Numerade Educator
01:29

Problem 87

In stable equilibrium, a body has
(b) minimum potential.
(a) maximum potential.
(c) equipotential.
(d) None of these

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:54

Problem 88

Mud thrown on a wall and sticking to it is an example for:
(a) Inelastic collision
(b) Elastic collision
(c) Super elastic collision
(d) Perfectly inelastic collision

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:26

Problem 89

Collision between two carom coins is an example for:
(a) Oblique collision
(b) Perfectly inelastic collision
(c) Inelastic collision
(d) Elastic collision

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:47

Problem 90

When a light body collides with a massive body at rest
(a) The light body rebounds after collision.
(b) The light body Cemains at rest.
(c) The massive body rebounds after collision.
(d) No reaction happens.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:58

Problem 91

When a massive body collides against a light body at rest
(a) The light body starts moving.
(b) The light body rebounds.
(c) The velocity of the bodies gets exchanged.
(d) The massive body comes to rest.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:35

Problem 92

Comets moves around the Sun in a highly elliptical orbit. The gravitational force on the comet due to the Sun is not normal to the comet's velocity in general. Yet the work done by the gravitational force over every orbit of the comet is zero. Why?
(a) The gravitational force is conservative, hence work done is zero.
(b) The gravitational force is non-conservative, hence work done is zero.
(c) Energy is absent, hence work done is zero.
(d) Force is in negative direction.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:31

Problem 93

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:
(a) Zero
(b) $\frac{M L^{2}}{k}$
(c) $\frac{K L^{2}}{2 M}$
(d) $\sqrt{M K L}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:20

Problem 94

A rubber ball is dropped from a height of $5 \mathrm{~m}$ on a plane, where the acceleration due to gravity is not shown. On bouncing it rises to $1.8 \mathrm{~m}$. The ball loses its velocity on bouncing by a factor of:
(a) $\frac{16}{5}$
(b) $\frac{2}{5}$
(c) $\frac{3}{5}$
(d) $\frac{9}{25}$

Ajay Singhal
Ajay Singhal
Numerade Educator
02:20

Problem 95

A ball of mass $\mathrm{m}$ moving with a constant velocity strikes against a ball of same mass at rest. If $e=$ coefficient of restitution, then what will be the ratio of velocity of two balls after collision?
(a) $\frac{1-e}{1+e}$
(b) $\frac{e-1}{e+1}$
(c) $\frac{1+e}{1-e}$
(d) $\frac{2+e}{e-1}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:26

Problem 96

A spltere of mass $8 \mathrm{~m}$ collides elastically (in one dimension) with a block of mass $2 \mathrm{~m}$. If the initial energy of sphere is $E$. What is the final energy of sphere?
(a) $0.8 \mathrm{E}$
(b) $0.36 \mathrm{E}$
(c) $0.08 \mathrm{E}$
(d) $0.64 \mathrm{E}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:17

Problem 97

Two balls, each with mass $2 \mathrm{~kg}$, and velocities of $2 \mathrm{~m} / \mathrm{s}$ and $3 \mathrm{~m} / \mathrm{s}$ collide head-on. Their final velocities are
$2 \mathrm{~m} / \mathrm{s}$ and $1 \mathrm{~m} / \mathrm{s}$, respectively. Is this collision elastic or inelastic?
(a) Collision is inelastic.
(b) Collision is elastic.
(c) Collison is perfectly elastic.
(d) Cannot be determine.

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:21

Problem 98

An object of mass $m_{1}=2 \mathrm{~kg}$, moving with velocity $v_{i 1}=12 \mathrm{~m} / \mathrm{s}$, collides head-on with a stationary object whose mass is $m_{2}=6 \mathrm{~kg}$. Given that the collision is elastic, what are the final velocities of the two objects. Neglect friction.
(a) $-6 \mathrm{~m} / \mathrm{s}$ and $+6 \mathrm{~m} / \mathrm{s}$
(b) $6 \mathrm{~m} / \mathrm{s}$ and $-6 \mathrm{~m} / \mathrm{s}$
(c) $6 \mathrm{~km} / \mathrm{s}$ and $-6 \mathrm{~km} / \mathrm{s}(\mathrm{d})-6 \mathrm{~km} / \mathrm{s}$ and $6 \mathrm{~km} / \mathrm{s}$

Vishal Gupta
Vishal Gupta
Numerade Educator
03:55

Problem 99

A bullet of mass $m=12 \mathrm{~g}$ strikes a stationary wooden block of mass $M=5.2 \mathrm{~kg}$ standing on a frictionless surface. The block, with the bullet embedded in it, acquires a velocity of $v=1.7 \mathrm{~m} / \mathrm{s}$. What was the velocity of the bullet before it struck the block? What fraction of the bullet's initial kinetic energy is lost (i.e., dissipated) due to the collision with the block?
(a) $387.4 \mathrm{~m} / \mathrm{s}$ and $0.9977$
(b) $738.4 \mathrm{~m} / \mathrm{s}$ and $0.9977$
(c) $738.4 \mathrm{~m} / \mathrm{s}$ and $0.7799$
(d) $387.4 \mathrm{~m} / \mathrm{s}$ and $0.7799$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:09

Problem 100

Two objects slide over a frictionless horizontal surface. The first object, mass $m_{1}=5 \mathrm{~kg}$, is propelled with speed $v_{i 1}=4.5 \mathrm{~m} / \mathrm{s}$ towards the second object, mass $m_{2}=2.5 \mathrm{~kg}$, which is initially at rest. After the collision, both objects have velocities which are directed $\theta=30^{\circ}$ on either side of the original line of motion of the first object. What are the final speeds of the two objects? Is the collision elastic or inelastic?
$$
\begin{array}{llll}
& \begin{array}{l}
\text { Speed of first } \\
\text { body }
\end{array} & \begin{array}{l}
\text { Speed of sec- } \\
\text { ond body }
\end{array} & \text { Collision } \\
\hline \text { (a) } & 5.1962 \mathrm{~m} / \mathrm{s} & 2.5981 \mathrm{~m} / \mathrm{s} & \text { elastic } \\
\hline \text { (b) } & 2.5981 \mathrm{~m} / \mathrm{s} & 5.1962 \mathrm{~m} / \mathrm{s} & \text { inelastic } \\
\hline \text { (c) } & 2.5981 \mathrm{~m} / \mathrm{s} & 5.1962 \mathrm{~m} / \mathrm{s} & \text { elastic } \\
\hline \text { (d) } & 5.1962 \mathrm{~m} / \mathrm{s} & 2.5981 \mathrm{~m} / \mathrm{s} & \begin{array}{l}
\text { Cannot } \\
\text { determine }
\end{array}
\end{array}
$$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:56

Problem 101

A skater of mass $M=120 \mathrm{~kg}$ is skating across a pond with uniform velocity $v=8 \mathrm{~m} / \mathrm{s}$. One of the skater's friends, who is standing at the edge of the pond, throws a medicine ball of mass $m=20 \mathrm{~kg}$ with velocity $u=3 \mathrm{~m} / \mathrm{s}$ to the skater, who catches it. The direction of motion of the ball is perpendicular to the initial direction of motion of the skater. What is the final speed of the skater? What is the final direction of motion of the skater relative to his/her initial direction of motion? Assume that the skater moves without friction.
(a) $8.76 \mathrm{~m} / \mathrm{s}, 8.35^{\circ}$
(b) $8.76 \mathrm{~m} / \mathrm{s}, 5.38^{\circ}$
(c) $6.87 \mathrm{~m} / \mathrm{s}, 3.58^{\circ}$
(d) None of these

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator