Irodov Problems in Physics Solutions Part 1

431 Pages·2016·8.02 MB·English

Solutions to
LE. Irodov’s
Problems in
General Physics

Volume I
Mechanics ¢ Heat ¢ Electrodynamics

SECOND EDITION

ABHAY KUMAR SINGH

Director
‘Abhay's 1. Physics Teaching Centra

cBSs

CBS PUBLISHERS & DISTRIBUTORS

4896/14, 11 DARYAGANY, NEW DELHI - 110 002 {INDIA}
Dedicated to
my Teacher

Prof. (Dr.) J. Thakur

(Department of Physics,
Patna University,
Palna-4)

ISBN :81-239.0399-5

First Edition ; 1995
Reprint: 1997
Second Edition : 1998
Reprint : 2000
Repriat: 2001
Reprint : 2002
Reprint : 2003
Reprint: 2004
Reprint: 2005

Copyright © Author & Publisher

AID rights reserved. No puri of this book may. be reproduced or
transmitted in any form or by any means, electronic or mechanical
including photocopying, recording, or any information storage and
retrieval system without permission, in weiting, from the publisher.

Published by 8.K. Jain for CBS Publishers & Distributors,
4596/14, U Darya Ganj, New Delhi - 110 002 (india)

Printed at
India Binding House, Delhi - 10032
FOREWORD

Science, in general, and physics, in particular, have evolved out of man's quest to know beyond
unknowns. Matter, radiation and their mutual interactions are basically studied in physics.
Essentially, this is an experimental science. By observing appropriate phenomena in natufe one
arrives at a set of rules which goes to establish some basic fundamental concepts, Entire physics
rests on them, Mere knowledge of them is however not enough. Ability to apply them to real
day-to-day problems is required. Prof. Irodov’s book contains one such set of numerical
exercises sproad over a wide spectrum of physical disciplines, Some of the problems of the book
Jong appeared to be notorious to pase serious challenges to students as well as to their teachers.
This book by Prof. Singh on the solutions of problems of Irodov's book, at the outset, scems
to remove the sonse af awe which at one time prevailed, Traditionally a difficult excicise 10
solve continues to draw the attention of concerned persons aver a sufficiently long time. Once
a logical solution for it becomes available, the difficulties associaled with its solutions are
forgotten very soon. This statement is not only valid for the solutions of simple physical probloms
but also to various physical phenomena,

Nevertheless, Prof. Singh’s attempt to write a book of this magnitude deserves an all out
praise, His ways of solving problems are elegant, straight forwerd, simple and direct, By writing
this book he has definitely contributed (o the cause of physics education, A word of advice to
iis users is hawever necessary. The solution to a particular problem as given in this book is
never to be consulted unless an all out effort in solving it independently has beon already made.
Only by such judicious nses of this book one would be able to reap better benefits out of it

‘AS a teacher who has tanght physics and who has been in touch with physies curricula
al Li.T,, Delhi for over thirty years, I earnestly feel that this book will certainly be of benefit
to younger students in theie formative years

Dr. Dilip Kumar Roy
Professor of Physics

Indian Institute of Technology, Delhi
New Delhi-1 10016,
FOREWORD

A proper understanding of the physical taws and principles that govern nature require
solutions of related problems which exemplify the principle in question and leads to a
better grasp of tho principles involved. It is only through experiments or through solutions
of multifarious problem-oriented questions can a student master the intricacies and fall
outs of a physical law, According to Ira M. Freeman, professor of physics of the state
university of new Jersy at Rutgers and author of “‘physic~principles and Insights”? --
“In certain situations mathematical formulation actually promotes intuilive understand-
ing...... Sometimes a mathematical forrmulation is not feasible, so that ordinary language
ust take the place of ntathematics in both roles. However, Mathematics is far more
rigorous and its concepts more precise than those of language. Any science that is able
to make extensive use of mathematical symbolism and procedures is justly cafled an exact
science’, I.E, Irodov’s problems in Gencral Physics fulfills such a need. This book
originally published in Russia contains about 1900 problems on mechanics, thermody-
namics, molecular physics, electrodynamics, waves and oscillations, optics, alomic and
suclear piysics. The book has survived the test of class room for many years as is evident
from its munber of reprint editions, which have appeared since the first English edition
of 198i, including an Indian Edition at alfordable price for Indian students.

Abhay Kumar Singh’s present book containing solutions to Dr. LE. Iradov’s Problems
in General Physics is a welcome altempt to develop a studeni’s problem solving skills.
The book should be very useful for the students studying a gencral course in physics and
also in developing their skills to answer questions normally encountered in national level
entrance exantinations conducted each year by various bodies for admissions to profes-
sional colleges in science and technology.

BP. PAL
Professor of Physics
ILT,, Delhi
PREFACE TO THE SECOND EDITION

Nothing succeeds like success, they say. Now, consequent upon the warm
welcome on the part of students and the teaching fraternity this revised and
enlarged edition of this volume is before you. In order to make it more up-to-date
and viable, a large mumber of problems have been streamlined with special focus
on ihe complicated and ticklish ones, to cater to the needs of the aspiring students,

I extend my deep sense of gratitude to all those who have directly or
indirecily engineered the cause of its existing status in the book world.

Paina
June 1997 Abhay Kumar Singh
PREFACE TO THE FIRST EDITION

When you invisage to write a book of solutions to problems, one pertinent question crops op
in the mind that—why solution! Is this 10 prave one’s erudition? My only defence against
this is thut the solution is a challenge to save the scientific man hours by channelizing thoughts
in a tight direction,

‘The book entitled “Problems in General Physics” authored by LE. lrodov (a noted
Russian physicist and mathematician) contains 1877 intriguing problems divided into six
chapters.

After the acceptance of my first book “Problems in Physics”, published by Wiley
Eastern Limited, I have got the courage 0 acknowledge the fact that good and honest
ultimately win in the market place. This stimufation provided me insight 1o come up with my
second attempt—"Solutions to I.E, Irodov’s Problems in General Physics.””

This first volume encompasses solutions of first three chapters containing 1052
problems. Although a large number of problems can be solved by different methods, [ have
adopted standard methods and in many of the problems with helping hints for other methods.

In the solutions of chapter three, the emf of a cell is represented by & (xi) in contrast
to the notation used in figures and in the problem book, due to some printing difficulty.

T am thankful to my students Mr, Omprakash, Miss Neera and Miss Punam for their
valuable co-operation even in my hard days while authoring the present book. I am also
thankful to my younger sister Prof, Ranju Singh, my younger brother Mr. Ratan Kumar Singh,
my junior friend Miss Anopama Bharti, other well wishers and frieads for their emotional
support. At last and above aff I am grateful to my Ma and Pappaji for their blessings and
encouragement,

ABHAY KUMAR SINGH.
CONTENTS

Foreword
Preface to the second edition
Preface to the first edition

PART ONE
PHYSICAL FUNDAMENTALS OF MECHANICS

1.1 Kinematics
1,2 ‘The Fundamentat Equation of Dynamics

1.3 Laws of Conservation of Energy, Momemtum, and Angular Momentum
14 Universal Gravitation

1.5. Dynamics of a Solid Body

1,6 Elastic Deformations of a Solid Body

1.7 Hydrodynamics

1.8 Retativistic Mechanics

PART TWO
‘THERMODYNAMICS AND MOLECULAR PHYSICS

2.1 Equation of the Gas State, Processes
2.2. The first Law of Thermodynamics. Heat Capacity

23 Kinetic theory of Gases, Boltzmann's Law and Maxwell's Distribution
2.4 The Second Law of Thermodynamics. Entropy

25 Liquids. Capiilary Effects

2.6 Phase Transformations

2.7 Transport Phenomena

PART FHREE
ELECTRODYNAMICS

3.1. Constant Electric Field ia Vacuum
3.2 Conductors and Dielectrics in an Electric Field

33. Electric Capacitance. Energy of an Electric Fiekd

3.4. Electric Current

3.5 Constant Magnetic Field. Magnetics

3.6 Electromagnetic induction, Maxwell's Equations

3.7 Motion of Charged Particles in Electric und Magnetic Fields

134
35-65
66-101
102-117
118-143
144-155
156-167
168-183

184-195
196-212
213-226
227-241
242-247
248-256
257-266

267-288

325-353
354.379
380-407
408-424
PHYSICAL FUNDAMENTALS OF MECHANICS

1.1 KINEMATICS
11 Let v, be the stream velocity and ¥ the velocity of motorboat with respect to water. The
motorbost reached point B while going downstream with velocity (v, + v))and thea retumed
with velocity (v' - v,) and passed the raft at point C. Let # be the time for the raft (which
flows with stream with velocity v,) 10 move front point A to C, during which the motorboat
moves from A to B and then from B t0 C.

=(Vgt VN weeny

A 7 B M0
—1 3% >
20 —

‘On solving we get ¥,=

12 Let s be the tow distance traversed by the point and , the time taken to cover half the
distance, Further let 2z be the time to cover the rest hal of the distance,

5 5
Therefore Fr hore @
5 s
and Brite of Be ae Q
‘Hence the sought average velocity
eee te 8 td
Ree” PDFs wl yrs dy,

13 As the cat starts ftom rest and finally comes a stop, and the rate of acceleration and
deceleration are equal, the distances as well as the times taken are same in these phases
of motion,

Let At be the time for which the car moves uniformly. Then the acceferalion / deceleration

Hat

time is each. So,
a
eve tm 2d y= EAD) gy
204 2
or ata P_AOPE
”
Hence bee vV 1-482 oss,
wr
14 (a) Sought average velocity gn
S_ em Es r
<ve~ £~ BES 10 em/s +
ny &
(©) For the maximum velocity, # shoutd be
ds. ‘, 10)
maximus, From the figure $f is maximus for
all points on the line ‘ac, thus the sought tl
maximum velocity becomes average velocity >
for the line ac and is equal to : r 10 20 5S
be _ 100.em
Be oe 035 emis

(©) Time fy shoutd be such that corresponding to it the slope S snows ‘pass through the

point O (origin), to satisty the relationship & z From figute the tangent at point d

passes through the origin and thus comesponding time t= f= 165.
1.5 Let the particles collide at the point A (Fig.), whose position vector is 7; (say), If t be the
time taken by each particle to reach at point A, from triangle law of vector addition :

Ho ein ote A
so, ge G-ae (o) ¢ yt
react
therefore, ge poke > =
eee ® % int
From Eqs. (1) aud (2)
oo ip placa
Fy=Py— (3-0) ) eae ra
yee? OTT fo) te
ot %
on, ph = 3071 which is the cought celationship.
bel 2-H °
16 We have ae
Pay @

From the vector diagram [of Bq. (1)) and using properties of triangle
ug

va Vibe Pa2ryrcosg = 39.7km/bt (2)

and vv og, singe SE
sin(e-@)” sin v
or @= sin”

Using (2) and putting the values of » and d

6-19.
Let one of the swimmer (say 1) cross the river along AB, which is obviously the shortest
path, Time taken to cross the river by the swimmer 1

42 =

Vvrw
For the other ewimmer (say 2), which follows the quickest path, the tine taken to
cross the river.

, (where AB™ d is the width of the river) a

any 2)

in the time ¢ drifting of the swimmer 2, becomes

%
a Mqh= 7d (using Ea. 2) @
Uf be the time for swimmer 2 to walk the distance ¥ to come from C toB Gig.) hen
vd
0
eae ©
According to the problem f= fy +t5
ad

or,

On solving we get