IIT JEE PHYSICS - Concepts Of Physics
IIT JEE PHYSICS(1978–2018: 41 Years)Topic-wise Complete SolutionsCombined VolumeMechanics, Waves and OpticsHeat, Electromagnetism and Modern PhysicsJitender SinghShraddhesh ChaturvediPsiPhiETC2018
iiPublished by PsiPhiETC116, Nakshatra Colony, BalapurHyderbad 500005, Telangana, India.IIT JEE PhysicsCopyright c 2018 by AuthorsAll rights reserved.No part of this publication may be reproduced or transmitted in any form or by anymeans, electronic or mechanical, including photocopy, recording, or any informationstorage and retrieval system, without permission in writing from the authors.Request for permission to make copies of any part of the work should be mailed to:116, Nakshatra Colony, Balapur, Hyderbad 500005, Telangana, India.The authors have taken care in preparation of this book, but make no expressed orimplied warranty of any kind and assume no responsibility for errors or omissions.No liability is assumed for incidental or consequential damages in connection withor arising out of the use of the information contained herein.Typeset in TEX.Third Edition, 20181ISBN 978-93-5281-484-8Printed in IndiaMRP 795 (incl. of all taxes)Visit us at: www.concepts-of-physics.com
We dedicate this book to the hundreds of anonymous professors at IITswho formulated the challenging problems for IIT-JEE. The book is ashowcase of their creation.
vForewordPhysics starts with observing the nature. The systematic observation results insimple rules which unlock the doors to the nature’s mystery. Having learned ahandful of simple rules, we can combine them logically to obtain more complicatedrules and gain an insight into the way this world works. The skill, to apply thetheoretical knowledge to solve any practical problem, comes with regular practiceof solving problems. The aim of the present collection of problems and solutions isto develop this skill.IIT JEE questions had been a challenge and a center of attraction for a big sectionof students at intermediate and college level. Independent of their occurrence asan evaluation tool, they have good potential to open up thinking threads in mind.Jitender Singh and Shraddhesh Chaturvedi have used these questions to come upwith a teaching material that can benefit students. The explanations accompanyingthe problems could bring conceptual clarity and develop the skills to approach anyunseen problem, step by step. These problems are arranged in a chapter sequencethat is used in my book Concepts of Physics. Thus a student using both the bookswill find it as an additional asset.Both Jitender Singh and Shraddhesh Chaturvedi have actually been my studentsat IIT, Kanpur. Jitender Singh has been closely associated with me since long. Itgives me immense pleasure to see that my own students are furthering the cause ofPhysics education. I wish them every success in this work and expect much morecontribution from them in future!Dr. H C VermaProfessor of PhysicsIIT Kanpur
viiPrefaceThis book provides a comprehensive collection of IIT JEE problems and their solutions. We have tried to keep our explanations simple so that any reader, with basicknowledge of intermediate physics, can understand them on his/her own withoutany external assistance. It can be, therefore, used for self-study.To us, every problem in this book, is a valuable resource to unravel a deeper understanding of the underlying physical concepts. The time required to solve a problemis immaterial as far as Physics is concerned. We believe that getting the right answeris often not as important as the process followed to arrive at it. The emphasis in thistext remains on the correct understanding of the principles of Physics and on theirapplication to find the solution of the problems. If a student seriously attempts allthe problems in this book, he/she will naturally develop the ability to analyze andsolve complex problems in a simple and logical manner using a few, well-understoodprinciples.For the convenience of the students, we have arranged the problems according tothe standard intermediate physics textbook. Some problems might be based onthe concepts explained in multiple chapters. These questions are placed in a laterchapter so that the student can try to solve them by using the concept(s) frommultiple chapters. This book can, thus, easily complement your favorite text bookas an advanced problem book.The IIT JEE problems fall into one of the nine categories: (i) MCQ with singlecorrect answer (ii) MCQ with one or more correct answers (iii) Paragraph based(iv) Assertion Reasoning based (v) Matrix matching (vi) True False type (vii) Fillin the blanks (viii) Integer Type, and (ix) Subjective. Each chapter has sectionsaccording to these categories. In each section, the questions are arranged in thedescending order of year of appearance in IIT JEE.Detailed solutions are given for each problem. We advise you to solve each problemyourself. You may cover the solution with a piece of paper to focus your attention tothe problem. If you can’t solve a problem, you can always look at the solution later.However, trying it first will help you identify the critical points in the problems,which in turn, will accelerate the learning process. Furthermore, it is advised thateven if you think that you know the answer to a problem, you should turn to itssolution and check it out, just to make sure you get all the critical points.This book has a companion website, www.concepts-of-physics.com. The site willhost latest version of the errata list and other useful material. We would be gladto hear from you for any suggestions on the improvement of the book. We havetried our best to keep the errors to a minimum. However, they might still remain!So, if you find any conceptual errors or typographical errors, howsoever small andinsignificant, please inform us so that it can be corrected in the later editions. Webelieve, only a collaborative e ort from the readers and the authors can make thisbook absolutely error-free, so please contribute.Many friends and colleagues have contributed greatly to the quality of this book.First and foremost, we thank Dr. H. C. Verma, who was the inspiring force behindthis project. Our close friends and classmates from IIT Kanpur, Deepak Sharma,Chandrashekhar Kumar and Akash Anand stood beside us throughout this work.This work would not have been possible without the constant support of our wivesReena and Nandini and children Akshaj, Viraj and Maitreyi.Jitender Singh, jsinghdrdo@gmail.comShraddhesh Chaturvedi, shraddhesh8@gmail.com
ContentsIMechanics . . . . . . . . . . . . . . . . . . . . . . . .122 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2971Units and Measurements . . . . . . . . . . . . . . . . . . .323 Laws of Thermodynamics . . . . . . . . . . . . . . . . . . 3022Rest and Motion: Kinematics . . . . . . . . . . . . . . .924 Specific Heat Capacities of Gases . . . . . . . . . . . 3093Newton’s Laws of Motion . . . . . . . . . . . . . . . . . .1925 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3294Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255Circular Motion . . . . . . . . . . . . . . . . . . . . . . . . . .366Work and Energy . . . . . . . . . . . . . . . . . . . . . . . . .417Centre of Mass, Linear Momentum, Collision .538Rotational Mechanics . . . . . . . . . . . . . . . . . . . . . .749Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119V Electromagnetism . . . . . . . . . . . . . . . . . 34526 Electric Field and Potential . . . . . . . . . . . . . . . . 34727 Gauss’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36528 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38029 Electric Current in Conductors . . . . . . . . . . . . . 39010 Simple Harmonic Motion . . . . . . . . . . . . . . . . . . 13030 Thermal and Chemical E ects of ElectricCurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41411 Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . 14831 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 41812 Some Mechanical Properties of Matter . . . . . . . 16532 Magnetic Field due to a Current . . . . . . . . . . . . 437II Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17733 Permanent Magnets . . . . . . . . . . . . . . . . . . . . . . . 45213 Wave Motion and Waves on a String . . . . . . . . 17934 Electromagnetic Induction . . . . . . . . . . . . . . . . . 45814 Sound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19235 Alternating Current . . . . . . . . . . . . . . . . . . . . . . . 48315 Light Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21336 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . 490III Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231VI Modern Physics . . . . . . . . . . . . . . . . . . . 49116 Geometrical Optics . . . . . . . . . . . . . . . . . . . . . . . . 23337 Electric Current through Gases . . . . . . . . . . . . . 49317 Optical Instruments . . . . . . . . . . . . . . . . . . . . . . . 27338 Photoelectric E ect and Wave-Particle Duality 49518 Dispersion and Spectra . . . . . . . . . . . . . . . . . . . . 27539 Bohr’s Model and Physics of the Atom . . . . . . 50519 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27840 X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52141 Semiconductors and Semiconductor Devices . . 526IV Thermodynamics . . . . . . . . . . . . . . . . . . 27942 The Nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52920 Heat and Temperature . . . . . . . . . . . . . . . . . . . . . 281A Quick Reference Formulae . . . . . . . . . . . . . . . . . . 54921 Kinetic Theory of Gases . . . . . . . . . . . . . . . . . . . 290ix
Part IMechanics Lm vM1
Chapter 4FrictionOne Option CorrectWe encourage you to show that if P P1 then the blockstarts sliding down and if P P2 then block startsmoving up. Note that P1 0 because tan µ.Ans. AQ 1. A block of mass m is on an inclined plane of angle . The coefficient of friction between the block and theplane is µ and tan µ. The block is held stationary byapplying a force P parallel to the plane. The directionof force pointing up the plane is taken to be positive.As P is varied from P1 mg(sin µ cos ) to P2 mg(sin µ cos ), the frictional force f versus P graphwill look like(2010)Q 2. What is the maximum value of the force F suchthat the block shown in the arrangement does notmove? [Take g 10 m/s2 .](2003)F60p3 kgµ 21p3m(A) 20 N (B) 10 N (C) 12 N (D) 15 NPSol. The forces acting of the block are applied force F ,weight mg, normal reaction N , and the frictional forcef as shown in the figure. (A) f(B) fP2P1(C)PP1(D)fP1NPfP1PP2P2P2mgSol. The forces acting on the block are its weightmg, normal reaction N , applied force P and frictionalforce f .F sin 60Resolve F in the horizontal and the vertical directions and apply Newton’s second law to getNPfmg sin mgmg cos f F cos 60 .(2)Fmax P mg sin .Q 3. An insect crawls up a hemispherical surface veryslowly (see figure). The coefficient of friction betweenthe surface and the insect is 1/3. If the line joining thecentre of the hemispherical surface to the insect makesan angle with the vertical, the maximum possiblevalue of is given by(2001)This is a straight line with slope 1. Substitute thevalues of P1 and P2 in equation (1) to get the frictionalforce at these points i.e.,f2 µmg 20 N.cos 60µ sin 60Ans. A(1)and(3)Eliminate f and N from equations (1)–(3) to getmg sin ,f1 µmg cos ,(1)f µN.which givesf N F sin 60 mg,The force F becomes maximum when the friction forcef attains its maximum value i.e.,Resolve mg along and normal to the inclined planeand apply Newton’s second law to get0 P fF cos 60fPµmg cos .25
26Part I. MechanicsSol. Lubrication reduces the non-conservative frictional forces. This increases the efficiency of the machine.Ans. B (A) cot 3(C) sec 3(B) tan 3(D) cosec 3Sol. The forces on the insect are its weight mg, normalreaction N , and the frictional force f .N cos f mg mgsinQ 6. A block of mass 2 kg rests on a rough inclinedplane making an angle of 30 with the horizontal. Thecoefficient of static friction between the block and theplane is 0.7. The frictional force onpthe block is (1980)(A) 9.8 N p(B) 0.7 9.8 3 N(C) 9.8 3 N (D) 0.7 9.8 NSol. The forces on the block of mass m 2 kg areits weight mg, normal reaction N , and the frictionalforce f . NmgfResolve mg along and perpendicular to the normal.Apply equilibrium condition to get3030 mg30(2)30osN mg cos .ingc(1)gsmf mg sin ,mThe angle attains its maximum value when the frictional force reaches its maximum limit of fmax µN .Substitute in equation (1) and then divide by equation (2) to get tan µ 1/3. Thus, cot 3.Ans. AThe net force on the block is zero because it is atrest. Resolve mg in the directions parallel and perpendicular to the inclined plane. Apply Newton’s secondlaw in these directions to getQ 4. A block of mass 0.1 kg is held against a wall byapplying a horizontal force of 5 N on the block. If thecoefficient of friction between the block and the wall is0.5, the magnitude of the frictional force acting on theblock is(1994)(A) 2.5 N (B) 0.98 N (C) 4.9 N (D) 0.49 NN mg cos 30 (2)(9.8)(0.866) 16.97 N,Sol. The forces on the block are applied force F 5 N,normal reaction N , weight mg and the frictional force f .fFNf mg sin 30 (2)(9.8)(0.5) 9.8 N.Note that f is less than fmax µN (0.7)(16.97) 11.88 N.Ans. AOne or More Option(s) CorrectQ 7. A small block of mass 0.1 kg lies on a fixed inclinedplane PQ which makes an angle with the horizontal.A horizontal force of 1 N acts on the block through itscentre of mass as shown in the figure. The block remainsstationary if [Take g 10 m/s2 .](2012)QmgIn equilibrium, N F 5 N and f mg 0.1 9.8 0.98 N. Note that f is less than its maximumpossible value of fmax µN 0.5 5 2.5 N.Ans. BQ 5. If a machine is lubricated with oil,(1980)(A) the mechanical advantage of the machine increases.(B) the mechanical efficiency of the machine increases.(C) both its mechanical advantage and mechanical efficiency increases.(D) its efficiency increases, but its mechanical advantage decreases.1NO P(A) 45(B) 45 and frictional force acts on the block towards P(C) 45 and frictional force acts on the block towards Q(D) 45 and frictional force acts on the block towards Q
Chapter 4. Friction27Sol. The forces acting on the block are F 1 N towards the left, weight mg 0.1 10 1 N downwards,normal force N , and the frictional force f . Resolve Fand mg along and perpendicular to the inclined plane.fIn this case, the body will just start moving whenthe horizontal component of Fpull is equal to or greaterthan the maximum value of friction force i.e.,Fpull cos fpull µNpull .(1)Since there is no acceleration in the vertical directionFcosNpull mg NFpull sin .(2) Eliminate Npull from equations (1) and (2) to getFFpull µmg.cos µ sin mg ins F s g comNpushsin mgFpush When 45 , the net force that brings the blockdown isFd mg sin 1F cos p2fpush1p 0.2mgThus, the block is stationary if 45 . When 45 ,the force Fd 0, and hence the block has a tendencyto move down. Thus, the frictional force f acts on theblock upwards i.e., towards Q.Ans. A, CAssertion Reasoning TypeQ 8. Statement 1: It is easier to pull a heavy objectthan to push it on a level ground.Statement 2: The magnitude of frictional force depends on the nature of the two surfaces in contact.(2008)(A) Statement 1 is true, statement 2 is true; statement2 is a correct explanation for statement 1.(B) Statement 1 is true, statement 2 is true; statement2 is not a correct explanation for statement 1.(C) Statement 1 is true, statement 2 is false.(D) Statement 1 is false, statement 2 is true.Sol. Both, statement 1 and statement 2, are true butstatement 2 is not a correct explanation of statement 1.The forces acting on the body in pull case are shown inthe figure.NpullFpullThe forces acting on the body in push case areshown in the figure. In this case,Fpush cos fpush µNpush ,Npush mg Fpush sin ,µmgFpush .cos µ sin Note that Fpull Fpush µmg if 0.Ans. BQ 9. Statement 1: A cloth covers a table. Some dishesare kept on it. The cloth can be pulled out withoutdislodging the dishes from the table.Statement 2: For every action there is an equal andopposite reaction.(2007)(A) Statement 1 is true, statement 2 is true; statement2 is a correct explanation for statement 1.(B) Statement 1 is true, statement 2 is true; statement2 is not a correct explanation for statement 1.(C) Statement 1 is true, statement 2 is false.(D) Statement 1 is false, statement 2 is true.Sol. Both statements are true but statement 2 is nota correct explanation for statement 1. Generally, statement 1 is attributed to Newton’s first law but this isnot entirely correct. We encourage you to repeat thisexperiment by pulling the cloth slowly. The outcome ofexperiment depends on acceleration acloth of the cloth.N ffpullaclothmgmg
28Part I. MechanicsThe forces acting on the dish are its weight mg,normal reaction N , and the frictional force f . Maximum value of the frictional force isfmax µN µmg.are stationary if r otherwise they are moving. Consider the limiting case, r , when the blocks are atrest andf µN2 .By Newton’s second law, acceleration of the dish isadish f /m. If acloth is small then the cloth and thedish move together i.e., adish acloth . Maximum valueof acloth for the cloth and the dish to move together isgiven by(1)Apply Newton’s second law to m1 ,R m1 g sin ,(2)N1 m1 g cos ,(3)and to m2 ,acloth adish fmax /m µg.Beyond this limit, acloth adish µg and hence thecloth comes out leaving the dish on table.Ans. Bf R m2 g sin ,(4)N2 m2 g cos .(5)Eliminate R, N2 , and f from equations (1)–(5) to getMatrix or Matching TypeQ 10. A block of mass m1 1 kg and another blockof mass m2 2 kg are placed together on an inclinedplane with angle of inclination (see figure). Variousvalues of are given in Column I. The coefficient offriction between the block m1 and the plane is alwayszero. The coefficient of static and dynamic friction between the block m2 and the plane are equal to µ 0.3.In Column II expressions for the friction on block m2are given. Match the correct expression of the frictionin Column II with the angles given in Column I. Theacceleration due to gravity is denoted by g. [Given,tan(5.5 ) 0.1, tan(11.5 ) 0.2, tan(16.5 ) 0.3]. r tan1 tan1 µm2m1 m2 (0.2) 11.5 . tan1 0.3 21 2 Thus, for 5 and 10 , blocks are at rest withfrictional forcef R m2 g sin (m1 m2 )g sin .For 15 and 20 , blocks are moving with frictional forcef µN2 µm2 g cos ,(limiting value).(2014)Column I(P)(Q)(R)(S) Ans. P7!2, Q7!2, R7!3, S7!3Column II 5 10 15 20(1)(2)(3)(4)m2 g sin (m1 m2 )g sin µm2 g cos µ(m1 m2 )g cos Sol. The forces on the block of mass m1 are its weightm1 g, normal reaction from the inclined plane N1 , andthe reaction from the second block R.N1RN2fm1 gm2 gTrue False TypeQ 11. When a person walks on a rough surface, thefrictional force exerted by the surface on the person isopposite to the direction of his motion.(1981)Sol. To walk in the forward direction, the personpushes his foot backward. Thus, the foot has a tendency to move backward against the rough surface. Tooppose this movement, the friction force on the footacts in the forward direction. Note that the frictionalforce is the only horizontal force on the person. Thus,a person can accelerate in forward direction only if thefrictional force is forward.Ans. FR Similarly, forces on the block of mas
This book provides a comprehensive collection of IIT JEE problems and their solu-tions. We have tried to keep our explanations simple so that any reader, with basic knowledge of intermediate physics, can understand them on his/her own without any external assistance. It can be, therefore, used for self-study.
Atomic Structure for JEE Main and Advanced (IIT-JEE) m Jupiter (XI) 3 Prepared By: Er. Vineet Loomba (IIT Roorkee) (iv) Some were even scattered in the opposite direction at an angle of 180 [Rutherford was very much surprised by it and remarked that “It was as incredible as if you fired a 15 inch shell at a piece of
JEE 2004 MATHEMATICS PAPERS Note: The IIT’s have continued the practice, begun in 2003, of collecting back the JEE question papers from the candidates. At the time of this writing, the JEE 2004 papers were not officially available to the general public, either on a website or on paper. So the text of the questions taken here was based on
IIT agreed to be a part of this competition: As per knowledge at present IIT Guwahati , IIT Kharagpur have agreed and talks are in forward with IIT Varanasi and IIT Roorkee. Finance and Logistics: Cost when not hosting: Travel Cost for maximum 10 member team to and fro to the host college Cost when Hosting the event: Major Distribution
8. JEE (MAIN) 2015 Candidates who wish to appear in JEE (Advanced) 2015 must write Paper-1 of JEE (Main) 2015 which is likely to be held in the month of April 2015. Candidates may visit the website www.jeemain.nic.in for information about JEE (Main) 2015. 9. ELIGIBILITY CRITERIA FOR APPEARING IN JEE (ADVANCED) 2015
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