IIT JEE PHYSICS - Concepts of Physics

1 IIT JEE PHYSICS (1978 2018: 41 Years)Topic-wise Complete SolutionsCombined VolumeMechanics, Waves and OpticsHeat, Electromagnetism and Modern PhysicsJitender SinghShraddhesh ChaturvediPsiPhiETC2018iiPublished by PsiPhiETC116, Nakshatra Colony, BalapurHyderbad 500005, Telangana, JEE PhysicsCopyrightc 2018 by AuthorsAll rights 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 for permission to make copies of any part of the work should be mailed to:116, Nakshatra Colony, Balapur, Hyderbad 500005, Telangana, 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 liability is assumed for incidental or consequential damages in connection withor arising out of the use of the information contained in Edition, 2018 1 ISBN 978-93-5281-484-8 Printed in IndiaMRP|795 (incl.)

2 Of all taxes)Visit us dedicate this book to the hundreds of anonymous professors at IITswho formulated the challenging problems for IIT-JEE. The book is ashowcase of their 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 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 Singh and Shraddhesh Chaturvedi have used these questions to come upwith a teaching material that can benefit students.

3 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 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 KanpurviiPrefaceThis 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 basicknowledge of intermediate PHYSICS , can understand them on his/her own withoutany external assistance.

4 It can be, therefore, used for us, every problem in this book, is a valuable resource to unravel a deeper under-standing 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, 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.

5 This book can, thus, easily complement your favorite text bookas an advanced problem 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 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 , 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 book has a companion website, latest version of the errata list and other useful material.

6 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 friends and colleagues have contributed greatly to the quality of this 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 would not have been possible without the constant support of our wivesReena and Nandini and children Akshaj, Viraj and Mechanics .. 11 Units and Measurements .. 32 Rest and Motion: Kinematics.

7 93 Newton s Laws of Motion .. 194 Friction .. 255 Circular Motion .. 366 Work and Energy .. 417 Centre of Mass, Linear Momentum, Collision . 538 Rotational Mechanics.. 749 Gravitation .. 11910 Simple Harmonic Motion .. 13011 Fluid Mechanics .. 14812 Some Mechanical Properties of Matter .. 165II Waves .. 17713 Wave Motion and Waves on a String .. 17914 Sound Waves .. 19215 Light Waves .. 213 III Optics .. 23116 Geometrical Optics .. 23317 Optical Instruments .. 27318 Dispersion and Spectra .. 27519 Photometry .. 278IV Thermodynamics.. 27920 Heat and Temperature.. 28121 Kinetic Theory of Gases .. 29022 Calorimetry .. 29723 Laws of Thermodynamics .. 30224 Specific Heat Capacities of Gases .. 30925 Heat Transfer .. 329V Electromagnetism .. 34526 Electric Field and Potential .. 34727 Gauss s Law .. 36528 Capacitors .. 38029 Electric Current in Conductors .. 39030 Thermal and Chemical E ects of ElectricCurrent .. 41431 Magnetic Field.

8 41832 Magnetic Field due to a Current .. 43733 Permanent Magnets .. 45234 Electromagnetic Induction .. 45835 Alternating Current .. 48336 Electromagnetic Waves .. 490VI Modern PHYSICS .. 49137 Electric Current through Gases .. 49338 Photoelectric E ect and Wave-Particle Duality 49539 Bohr s Model and PHYSICS of the Atom .. 50540 X-rays .. 52141 Semiconductors and Semiconductor Devices .. 52642 The Nucleus.. 529A Quick Reference Formulae.. 549ixPart IMechanics m~vLM1 Chapter4 FrictionOne Option CorrectQ block of massmis on an inclined plane of angle .Thecoe cient of friction between the block and theplane is and tan > . The block is held stationary byapplying a forcePparallel to the plane. The directionof force pointing up the plane is taken to be varied fromP1=mg(sin cos )toP2=mg(sin + cos ), the frictional forcefversusPgraphwill look like(2010) mP(A)P1P2Pf(B)P1P2Pf(C)P1P2Pf(D) forces acting on the block are its weightmg, normal reactionN, applied forcePand mgsin Resolvemgalong and normal to the inclined planeand apply Newton s second law to get0=P+f mgsin ,which givesf= P+mgsin.

9 (1)This is a straight line with slope 1. Substitute thevalues ofP1andP2in equation (1) to get the frictionalforce at these points ,f1= mgcos ,andf2= mgcos .We encourage you to show that ifP<P1then the blockstarts sliding down and ifP>P2then block startsmoving up. Note thatP1>0 because tan > . Q is the maximum value of the forceFsuchthat the block shown in the arrangement does notmove? [Takeg= 10 m/s2.](2003)p3kgF60 =12p3(A) 20 N (B) 10 N (C) 12 N (D) 15 forces acting of the block are applied forceF,weightmg, normal reactionN, and the frictional forcefas shown in the 60 mgFsin 60 NfResolveFin the horizontal and the vertical direc-tions and apply Newton s second law to getN=Fsin 60 +mg,(1)f=Fcos 60 .(2)The forceFbecomes maximum when the friction forcefattains its maximum value ,f= N.(3)EliminatefandNfrom equations (1) (3) to getFmax= mgcos 60 sin 60 = 20 Q insect crawls up a hemispherical surface veryslowly (see figure). The coe cient of friction betweenthe surface and the insect is 1/3.

10 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)2526 Part I. Mechanics (A) cot = 3 (B) tan =3(C) sec = 3 (D) cosec = forces on the insect are its weightmg, normalreactionN, and the frictional forcef. =mgNfmgcos mgsin Resolvemgalong and perpendicular to the equilibrium condition to getf=mgsin ,(1)N=mgcos .(2)The angle attains its maximum value when the fric-tional force reaches its maximum limit offmax= in equation (1) and then divide by equa-tion (2) to get tan = =1/3. Thus, cot = Q block of mass kg is held against a wall byapplying a horizontal force of 5 N on the block. If thecoe cient of friction between the block and the wall , the magnitude of the frictional force acting on theblock is(1994)(A) N (B) N (C) (D) forces on the block are applied forceF= 5 N,normal reactionN, weightmgand the frictional equilibrium,N=F= 5 N andf=mg= N.