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ComprehensiveObjective

PHYSICSFor Competitive Examinations

Volume—I

GOLDEN BELLS(AN IMPRINT OF LAXMI PUBLICATIONS PVT. LTD.)

� BANGALORE � CHENNAI � COCHIN � GUWAHATI � HYDERABAD

� JALANDHAR � KOLKATA � LUCKNOW � MUMBAI � RANCHI

NEW DELHI


PHYSICSFor Competitive Examinations

Volume—I

By

NARINDER KUMARM.Sc. PES (I)

Department of PhysicsS.D. Govt. College

Ludhiana

&

Dr. J.K. JUNEJAM.Sc., M.Phil., Ph.D.

Department of PhysicsHindu College

Sonepat

RST

RST

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GBC-5008-495-OBJECTIVE PHYSICS I

All Rights Reserved with the Publisher.

Revised Edition, 2006Reprint, 2007

C—128/06/06

Laser Typesetted at : Goswami Printers, Delhi Printed at : Ajit Printers, Delhi.


PHYSICSVolume—I

Comprehensive Objective Physics is essential for all the students preparing for various Engineering & Medical En-trance Examinations given below and also for students preparing for other State Services Exams.

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*Please give full address of the Coaching Institute and Physics Teacher, with telephone numbers.Comprehensive Objective Physics—Volume—I

PREFACE TO THE SECOND EDITION

There is no dearth of competition books for engineering and medical entrance examinations. But there is no singlebook which completely satisfies the intelligent student. The present book is a serious attempt in this direction. We haveleft no stone unturned to get ‘EXTREMELY SATISFACTORY’ grade from the readers of the book.

Some salient features of the book are as under :(i) No superfluous question. Only those questions have been included which have either been already set in different

examinations or are expected to be set.(ii) Most systematic presentation. It is the only book in the market which has systematically categorised the study

material of each unit. The study material has been clearly demarcated in the following seven segments.1. SYNOPSIS2. SET I [Contains MCQs based on Memory Work, Hard Facts, Important Terms, Important Formulae etc.]3. SET II [Contains MCQs based on Important Basic Concepts, Application of Formulae and Brain Teasers]4. SET III [Contains MCQs with more than one correct alternative]5. SET IV [Contains MCQs based on Typical Numerical Bank]6. SELF-EVALUATION TEST I [Contains Expected Questions for Forthcoming Examinations]7. SELF-EVALUATION TEST IIIn addition to the above, ‘Knowledge Plus’ has also been included at some places.

(iii) Time-saving solutions. Special techniques have been used in solving questions. These techniques have been high-lighted at different places in the book. If the reader tries to grasp these techniques, considerable time will be saved.

The book has been divided into two volumes. The divisions are as under :

Units

Volume—I I—XTopics included

Mathematical Tools ; Introduction, Units, Measurements and Dimension ; Description of Motion in One Dimension ;Description of Motion in Two and Three Dimensions (Vectors ; Motion in Two and Three Dimensions) ; Laws ofMotion ; Work, Energy and Power ; Rotational Motion (Circular Motion ; Centre of Mass and Rotational Mechanics) ;Gravitation ; Properties of Matter (Elasticity ; Fluids at Rest ; Surface Tension ; Fluids in Motion ; Kinetic Theoryof Gases) ; Heat and Thermodynamics ; Oscillations and Waves.

Units

Volume—II XI—XVIIITopics included

Electrostatics ; Current Electricity ; Magnetic Effect of Current and Magnetism ; Electromagnetic Induction andAlternating Current ; Optics ; Dual Nature of Matter and Radiations ; Atomic Nucleus ; Solids and SemiconductorDevices, Electromagnetic Waves and Principles of Communication.3 Practice Papers are designed in such a way so as to enable the students to evaluate their skills in Volume—I andVolume—II separately.Model Test Papers based on full syllabus are included in Volume—II for Self Assessment.

Utmost effort has been made to make this book as best as possible. But it is our firm conviction that there is alwaysa scope for improvement. So, we invite your suggestions for the further improvement of the book. It would be ourearnest endeavour to incorporate all good suggestions in the next edition.

—AUTHORS

List of Chapters in Volume—I and Volume—II

Volume—I

Unit 0 MATHEMATICAL TOOLS

Unit I INTRODUCTION AND MEASUREMENT

1.01 Introduction, Units, Measurement and Dimension

1.02 Significant Figures and Error Analysis

Unit II DESCRIPTION OF MOTION IN ONE DIMENSION

Unit III DESCRIPTION OF MOTION IN TWO AND THREE DIMENSIONS

3.01 Vectors

3.02 Motion in Two and Three Dimensions

Unit IV LAWS OF MOTION

Unit V WORK, ENERGY AND POWER

Unit VI ROTATIONAL MOTION (Circular Motion, Centre of Mass and Rotational Mechanics)

Unit VII GRAVITATION

Unit VIII PROPERTIES OF MATTER

8.01 Elasticity

8.02 Fluids at Rest

8.03 Surface Tension

8.04 Fluids in Motion

8.05 Kinetic Theory of Gases

Unit IX HEAT AND THERMODYNAMICS

Unit X OSCILLATION AND WAVES

3 Practice Papers

Volume—II

Unit XI ELECTROSTATICS

Unit XII CURRENT ELECTRICITY

Unit XIII MAGNETIC EFFECT OF CURRENT AND MAGNETISM

Unit XIV ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

Unit XV OPTICS

Unit XVI DUAL NATURE OF MATTER AND RADIATIONS

Unit XVII ATOMIC NUCLEUS

Unit XVIII SOLIDS AND SEMICONDCUTOR DEVICES, ELECTROMAGNETIC WAVES ANDPRINCIPLES OF COMMUNICATION

3 Practice Papers

3 Model Test Papers based on Full Syllabus

Unit 0 MATHEMATICAL TOOLS 1

Unit I INTRODUCTION AND MEASUREMENT

CONTENTS

1.01. Introduction, Units, Measurements and Di-mension• Synopsis 15• Question Bank with Answers/Solutions

Set I : MCQs based on Memory Work, Hard 28Facts, Important Terms, ImportantFormulae etc.

Set II : MCQs based on Important Basic 41Concepts, Applications of Formulae,Brain Teasers

Set III : MCQs with More than one Correct 58Alternative

Set IV : MCQs based on Typical Numerical 60Bank (Exclusively for EngineeringEntrance Test)

1.02. Significant Figures and Error Analysis• Synopsis 64

• Question Bank with Answers/Solutions


Set II : MCQs based on Important Basic 74Concepts, Application of Formulae,Brain Teasers

Set III : MCQs based on Typical Numerical 79Bank (Exclusively for EngineeringEntrance Tests)

• Self-Evaluation Test I with Answers/ 80Solutions (Expected Questions forForthcoming Examinations)

• Self-Evaluation Test II with Answers/ 85Solutions

Unit II DESCRIPTION OF MOTION IN ONE DIMENSION

2. Description of Motion in One Dimension• Synopsis 93• Question Bank with Answers/Solutions



Set III : Graphical Bank (MCQs based on 130Graphs)

Set IV : MCQs with More than one Correct 144Alternative

Set V : MCQs based on Typical Numerical 148Bank (Exclusively for EngineeringEntrance Tests)



Unit III DESCRIPTION OF MOTION IN TWO AND THREE DIMENSIONS

3.01. Vectors• Synopsis 171• Question Bank with Answers/Solutions




Set IV : MCQs based on Typical Numerical 206Bank (Exclusively for EngineeringEntrance Tests)

3.02. Motion in Two and Three Dimensions• Synopsis 212• Question Bank with Answers/Solutions







Unit IV LAWS OF MOTION

4. Laws of Motion• Synopsis 261• Question Bank with Answers/Solutions



Set III : MCQs With More than one Correct 314Alternative




Unit V WORK, ENERGY AND POWER

5. Work, Energy and Power• Synopsis 351• Question Bank with Answers/Solutions







Unit VI ROTATIONAL MOTION

6. Circular Motion, Centre of Mass &Rotational Mechanics• Synopsis 419• Question Bank with Answers/Solutions







7. Gravitation• Synopsis 517• Question Bank with Answers/Solutions







Unit VII GRAVITATION

Unit VIII PROPERTIES OF MATTER

8.01. Elasticity• Synopsis 591• Question Bank with Answers/Solutions





8.02. Fluids at Rest• Synopsis 631• Question Bank with Answers/Solutions



Set III : MCQs with more than one Correct 654Alternative


8.03. Surface Tension• Synopsis 660• Question Bank with Answers/Solutions


Set II : MCQs based on Important Basic 671Concepts. Application of Formulae,Brain Teasers



8.04. Fluids in Motion• Synopsis 685• Question Bank with Answers/Solutions





8.05. Kinetic Theory of Gases• Synopsis 709• Question Bank with Answers/Solutions





• Self-Evaluation Test I with Answers/ 735Solutions (Expected Questions forForthcoming Examination)


9. Heat and Thermodynamics• Synopsis 749• Question Bank with Answers/Questions







Unit IX HEAT AND THERMODYNAMICS

Unit X OSCILLATIONS AND WAVES

10. Oscillations and Waves• Synopsis 851• Question Bank with Answers/Solutions







PRACTICE PAPERS BASED ON UNITS I—X

• Practice Paper 1 1• Practice Paper 2 7• Practice Paper 3 13

UNIT 0

*MATHEMATICAL TOOLS

Elementary concepts of differentiation and integration for describing motion.

1. GRAPHS

A diagrammatic representation of the variation ofone quantity with respect to another is called a graph. Agraph gives visual impression about how one quantity var-ies w.r.t. the other.

Suppose we want to depict the relation F = ma graphi-cally. If mass is regarded as constant, then F ∝ a. We knowthat the acceleration is determined by force. So, for the pur-pose of drawing a graph, force is the independent variableand acceleration is the dependent variable.

In any graph, the independent variable (thecause) is, by convention, represented along x-axis andthe dependent variable (the effect) is representedalong y-axis. Thus, in the problem under consideration,force will be plotted against x-axis and the acceleration willbe plotted against y-axis.

In order to plot a graph, we must have data, i.e., a setof values for the independent variable and of the correspondingvalues for the dependent variable. This data can be eitherexperimental or theoretical. The experimental data comprisesthe observed values of the quantities from an experiment.The theoretical data is obtained by feeding a particular valueof one quantity in a theoretical relationship and calculatingthe magnitude of the other quantity.

While drawing a graph, we have to choose a suitablescale. The scale chosen should be simple and convenient tooperate. It should not be so small that all the points of thedata get cramped together in a small portion of the graphpaper. The scale should also not be so large that the whole ofthe data cannot be represented on the graph paper.

2. USES OF GRAPHS

(i) From the shape of the graph, we can have a clearidea about the relationship between the two quantities

represented by it. If the graph is a straight line and passesthrough the origin, it is of the form y = mx. A straight linegraph having positive or negative intercepts on y-axis isrepresented by :

y = mx ± c(ii) The slope of the graph and its intercept on the x or

y-axis gives us the values of physical quantities.(iii) A graph helps in identifying the inaccuracies in

the experimental data.(iv) With the help of graph, we can determine the mean

value from a large number of observations.

3. TRIGONOMETRICAL FUNCTIONS

These are also known as trigonometric ratios orcircular functions of θ. The trigonometric function is so namedbecause to each value of θ, there corresponds one and onlyone value of a trigonometrical ratio of θ. It may be noted thateach trigonometrical ratio is a mere number.

Consider a revolving line which starts from OX andtraces out any ∠XOP = θ in the first quadrant.

From P, drop a perpendicular PM on X′OX. With dueregard to signs of OM, MP, OP, the trigonometrical ratios ofθ are defined as follows :

(i)MPOP

is called the sine of θ, written as sin θ ;

Y

XM

P

OX´

Y´

θ

Fig. 1

*Exclusively for those appearing in Medical Entrance Tests.

2 COMPREHENSIVE OBJECTIVE PHYSICS

(b) In the second quadrant, only the sine and (its re-ciprocal) cosecant are +ve.

(c) In the third quadrant, only the tangent and (itsreciprocal) cotangent are +ve.

(d) In the fourth quadrant, only the cosine and (itsreciprocal) secant are +ve.

Fig. 2 should serve as a good aid to memory.Let us now mention a few facts about the limits to the

values of T-ratios.(i) The maximum, i.e., greatest value of sin θ or cos

θ is 1. The minimum, i.e., least value of sin θ or cos θ is – 1.(ii) sec θ and cosec θ cannot be numerically less than

one.(iii) tan θ and cot θ can have any numerical values.

Aid to memory for values of T-ratios

0° 30° 45° 60° 90°

sine 02

12

22

32

42

*cosine 42

32

22

12

02

*sines written backwards.

5. T-RATIOS OF CERTAIN ALLIED ANGLES

An angle is said to be allied to an angle θ if their sumis 0°, or their sum or difference is a multiple of 90°.

I. sin (– θ) = – sin θ ; cos (– θ) = cos θ ;tan (– θ) = – tan θ ; cot (– θ) = – cot θ ;sec (– θ) = sec θ ; cosec (– θ) = – cosec θ

II. sin (90 – θ) = cos θ ; cos (90 – θ) = sin θ ;tan (90 – θ) = cot θ ; cot (90 – θ) = tan θ ;sec (90 – θ) = cosec θ ; cosec (90 – θ) = sec θ

III. sin (90 + θ) = cos θ ; cos (90 + θ) = – sin θ ;tan (90 + θ) = – cot θ ; cot (90 + θ) = – tan θ ;sec (90 + θ) = – cosec θ ; cosec (90 + θ) = sec θ

IV. sin (180 – θ) = sin θ ; cos (180 – θ) = – cos θ ;tan (180 – θ) = – tan θ ; cot (180 – θ) = – cot θ ;sec (180 – θ) = – sec θ ; cosec (180 – θ) = cosec θ

V. sin (180 + θ) = – sin θ ; cos (180 + θ) = – cos θ ;tan (180 + θ) = tan θ ; cot (180 + θ) = cot θ ;sec (180 + θ) = – sec θ ; cosec (180 + θ) = – cosec θ

VI. sin (270 – θ) = – cos θ ; cos (270 – θ) = – sin θ ;tan (270 – θ) = cot θ ; cot (270 – θ) = tan θ ;sec (270 – θ) = – cosec θ ; cosec (270 – θ) = – sec θ

VII. sin (270 + θ) = – cos θ ; cos (270 + θ) = sin θ ;tan (270 + θ) = – cot θ ; cot (270 + θ) = – tan θ ;sec (270 + θ) = cosec θ ; cosec (270 + θ) = – sec θ

(ii)OMOP

is called the cosine of θ, written as cos θ ;

(iii)MPOM

is called the tangent of θ, written as tan θ ;

(iv)OMMP

is called the cotangent of θ, written as cot θ ;

(v)OPOM

is called the secant of θ, written as sec θ ;

(vi)OPMP

is called the cosecant of θ, written as cosec θ.

Note. sin θ is not equal to sin × θ, i.e., sin is not a multiplier. Sinθ is a single symbol.

4. FUNDAMENTAL RELATIONS BETWEEN THET-RATIOS OF AN ANGLE

(i) cot θ = 1

tan θ(ii) sec θ =

1cos θ

(iii) cosec θ = 1

sin θ(iv) tan θ =

sincos

θθ

(v) cot θ = cossin

θθ

(vi) sin2 θ + cos2 θ = 1

(vii) sec2 θ = 1 + tan2 θ (viii) cosec2 θ = 1 + cot2 θ

Signs of T-ratios and Limits to the value of T-ratiosIn order to understand the signs of T-ratios, let us

first understand the rule for signs of the sides of the triangleOMP.

(i) OM is positive if it is drawn to the right of O andnegative if drawn to the left.

(ii) MP is positive if it is drawn above X′OX and nega-tive if drawn below X′OX.

(iii) OP is always positive.Keeping in mind this sign convention and the defini-

tions of T-ratios, we shall find that :(a) In the first quadrant, all the T-ratios are positive.

Y

XX´

Y´

O

SIN ALL

COSTAN

Fig. 2

MATHEMATICAL TOOLS 3

VIII. sin (360 – θ) = sin (– θ) = – sin θ ;cos (360 – θ) = cos (– θ) = cos θ ;tan (360 – θ) = tan (– θ) = – tan θ ;cot (360 – θ) = cot (– θ) = – cot θ ;sec (360 – θ) = sec (– θ) = sec θ ;cosec (360 – θ) = cosec (– θ) = – cosec θ

IX. sin (360 + θ) = sin θ ; cos (360 + θ) = cos θ ;tan (360 + θ) = tan θ ; cot (360 + θ) = cot θ ;sec (360 + θ) = sec θ ; cosec (360 + θ) = cosec θ.

Note 1. Each t-ratio of (n.360° + θ) is equal to the correspond-ing t-ratio of θ, n being any integer, +ve or –ve.

Note 2. Consider θ to be acute and find the quadrant in whichthe allied angle lies. The sign of the required t-ratio in this quadrant isthe required sign.

Note 3. If the allied angle is – θ or 180° ± θ, the t-ratio is notchanged in form. But if the allied angle is 90° ± θ or 270° ± θ, the t-ratiois changed in form.

Note 4. If the allied angle is 360° ± θ, subtract 360° from theangle and find the t-ratios of the resulting angle.

6. SOME IMPORTANT FORMULAE OF TRIGONO-METRY

(i) sin (A + B) = sin A cos B + cos A sin B(ii) cos (A + B) = cos A cos B – sin A sin B

(iii) tan (A + B) = tan A + tan B

1 tan A tan B−

(iv) sin (A – B) = sin A cos B – cos A sin B(v) cos (A – B) = cos A cos B + sin A sin B

(vi) tan (A – B) = tan A tan B

1 tan A tan B−

+

(vii) 2 sin A cos B = sin (A + B) + sin (A – B)(viii) 2 cos A sin B = sin (A + B) – sin (A – B)

(ix) 2 cos A cos B = cos (A + B) + cos (A – B)(x) 2 sin A sin B = cos (A – B) – cos (A + B)

(xi) sin C + sin D = 2 sin C + D

2C D

2cos

−

(xii) sin C – sin D = 2 cos C + D2

C D2

sin−

(xiii) cos C + cos D = 2 cos C + D2

C D2

cos−

(xiv) cos C – cos D = 2 sin C + D2

sinD C

2−

(xv) sin 2A = 2 sin A cos A(xvi) cos 2A = cos2 A – sin2 A

(xvii) cos 2A = 1 – 2 sin2 A (xviii) cos 2A = 2 cos2 A – 1

7. LOGARITHMS

Definition and notation of *LogarithmIf ax = N, then x is called the logarithm of N to the

base a. It is written as loga N. It is read as “log N to the basea.”

If ax = N, then loga N = x.So, logarithm of any number to a given base is the

power to which base must be raised to obtain that number.Illustration 1. ∵ 23 = 8∴ log2 8 = 3

Four formulae of LogarithmsI. loga mn = loga m + loga n (Product formula)

II. loga mn

= loga m – loga n (Quotient formula)

III. loga mn = n loga m (Power formula)IV. loga m = logb m × loga b (Base-changing formula)

8. TWO SYSTEMS OF LOGARITHMS

(i) Natural logarithms and (ii) Common logarithms.Logarithms to the base e are called natural loga-

rithms. These are used in theoretical calculations.e is the sum of the infinite series :

1 + 11

12

13! ! !

+ + + ......

Its value is 2.7182.Logarithms to the base 10 are called common loga-

rithms. These are used in arithmetical calculations.When the base of a logarithm is not mentioned, it is

understood to be 10. The word ‘logarithm’ generally meanscommon logarithm.

9. CHARACTERISTIC AND MANTISSA

The integral part of the logarithm of a number afterexpressing the decimal part as positive is called the charac-teristic. The positive decimal part is called the mantissa. Itis important to note that mantissa is always positive.

Illustration 2. The logarithm of a number is 2.3147.Find the characteristic and mantissa.

Sol. Since the decimal part of the logarithm is posi-tive,

∴ Characteristic = 2 and mantissa = .3147Illustration 3. The logarithm of a number is 0.2983.

Find the characteristic and mantissa.Sol. Since the decimal part of the logarithm is positive,∴ Characteristic = 0 and mantissa = .2983

*The literal meaning of the word ‘logarithm’ is to ‘cut downarithmetic’.

Comprehensive Objective Physics Vol.I For Competitive Examinations

Publisher : Laxmi Publications ISBN : 9788179680544Author : Prof. Narinderkumar, Dr. J. K. Juneja

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