IIT JEE PHYSICS (1978–2 (1978–2016 016:: 39 Years) Topic-wise Complete Solutions
Volume I Mechanics, Waves and Optics
Jitender Singh Shraddhesh Chaturvedi
PsiPhiETC 2016
ii c 2016 by Authors Copyright
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Typeset in TEX. Second Edition, 2016
ISBN 978-93-5265-609-7 Printed in India.
1.
We dedi dedica cate te this this book book to the the hundr undred edss of anonymous professors at IITs who formulated the chall hallen engi ging ng prob problem lemss fo forr IIT-J IIT-JEE EE.. The The book is a showcase of their creation.
v Foreword
Physics Physics starts with observing the nature. The systematic systematic observation observation results in simple rules which unlock the doors to the nature’s mystery. Having learned a handful of simple rules, we can combine them logically to obtain more complicated rules and gain an insight into the way this world works. The skill, to apply the theoretical knowledge to solve any practical problem, comes com es with with regula regularr pract practice ice of solvin solvingg proble problems. ms. The aim of the presen presentt collection of problems and solutions is to develop this skill. IIT JEE questions had been a challenge and a center of attraction for a big section of students at intermediate and college level. Independent of their occurrence as an evaluation tool, they have good potential to open up thinking threads in mind. Jitender Jitender Singh and Shraddhesh Shraddhesh Chaturve Chaturvedi di have used these questions to come up with a teaching material that can benefit students. The explanations accompanying the problems could bring conceptual clarity and develop the skills to approach any unseen problem, step step by step. step. These These problems problems are arrang arranged ed in a chapter hapter sequenc sequencee that that is used in my book Concepts Concepts of Physics. Physics. Thus Thus a student student using both the books will find it as an additional asset. Both Jitender Singh and Shraddhesh Chaturvedi have actually been my student studentss at IIT, Kanpur. Kanpur. Jitender Jitender Singh has been b een closely closely associated with me since long. It gives me immense pleasure pleasure to see that my own students students are furthering the cause of Physics education. I wish them every success in this work and expect much more contribution from them in future! Dr. H C Verma Professor of Physics IIT Kanpur
vii Preface
This 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 basic knowledge of intermediate physics, can understand them on his/her own without any 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 deeper unders understan tandin dingg of the underly underlying ing physica physicall concep concepts. ts. The time required to solve a problem is immaterial as far as Physics is concerned. We believe that getting the right answer is often not as important as the process process follow followed to arrive arrive at it. The emphasi emphasiss in this text text remain remainss on the correct understanding of the principles of Physics and on their application to find the solution of the problems. If a student seriously attempts all the problems in this book, he/she will naturally develop the ability to analyze and solve complex problems in a simple and logical manner using a few, well-understood principles. For the convenience of the students, we have arranged the problems according according to the standard intermed intermediate iate physics physics textbook. Some problems problems might mig ht be based based on the concept conceptss explai explained ned in multi multiple ple chapte chapters. rs. These These questions are placed in a later chapter so that the student can try to solve them by using the concept(s) from multiple chapters. This book can, thus, easily complement your favorite text book as an advanced problem book. The IIT JEE proble problems ms fall into one of the nine catego categorie ries: s: (i) MCQ with single correct answer (ii) MCQ with one or more correct answers (iii) Paragraph based (iv) Assertion Reasoning based (v) Matrix matching (vi) True False type (vii) Fill in the blanks (viii) Integer Type, and (ix) Subjecti Subjective ve.. Each Each chapter hapter has sectio sections ns accord according ing to these these categori categories. es. In each section, the questions are arranged in the descending order of year of appearance in IIT JEE. The solutio solutions ns are given given at the end of each each chapter hapter.. If you can’t solve solve a proble problem, m, yo you u can alway alwayss look at the solutio solution. n. Ho How wever, ever, trying trying it first first will help you identify the critical points in the problems, which in turn, will accelerate the learning process. Furthermore, it is advised that even if you think that you know the answer to a problem, you should turn to its solution 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 www.concepts-of-physics.com. The site will host latest version of the errata list and other useful material. We would be glad to hear from you for any suggestions on the improvement of the book. book. We hav have trie tried d our our best best to keep keep the the erro errors rs to a mi mini nim mum. um. How Ho wever, ever, they they mig might ht still remain! remain! So, if yo you u find any conceptu conceptual al errors errors or typographical errors, howsoever small and insignificant, please inform us so that that it ca can n be co corr rrec ecte ted d in the late laterr edit editio ions ns.. We belie believ ve, only only a
viii collaborative effort from the students and the authors can make this book absolutely error-free, so please contribute. Many friends and colleagues have contributed greatly to the quality of this this book. First First and foremo foremost, st, we thank Dr. H. C. Verm Verma, a, who was was the inspiring inspiring force behind this project pro ject.. Our close friends friends and classmates classmates from IIT Kanpur, Deepak Sharma, Chandrashekhar Kumar and Akash Anand stood stood besid besidee us thro throug ugho hout ut this this work. ork. This This work ork would ould not not hav have been been possible without without the constant constant support of our wives Reena and Nandini Nandini and children Akshaj, Viraj and Maitreyi. Jitender Singh,
[email protected] [email protected] [email protected] Shraddhesh Chaturvedi,
[email protected]
Contents
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
I
Mechanics . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
Units Units and Me Measu asure reme men nts . . . . . . . . . . . . . . . . . . . .
3
2
Rest Re st and and Moti Motion on:: Kinem Kinemati atics cs . . . . . . . . . . . . . . . . .
13
3
Newto Ne wton’s n’s Laws Laws of of Motio Motion n . . . . . . . . . . . . . . . . . . . .
29
4
Frict rictio ion n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
5
Circ Circul ular ar Moti Motion on . . . . . . . . . . . . . . . . . . . . . . . . . .
56
6
Work ork and and En Ener ergy gy . . . . . . . . . . . . . . . . . . . . . . . . .
65
7
Centre Centre of Mass, Mass, Linea Linear r Moment Momentum, um, Collis Collision ion . . . . . . .
83
8
Rotat Rotatio ional nal Me Mec chanics hanics . . . . . . . . . . . . . . . . . . . . . . . 116
9
Gra Gravitat vitatio ion n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
10 Simple Harmonic Motion . . . . . . . . . . . . . . . . . . . . 201 11 Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . 232 12 Some Mechanical Properties of Matter
. . . . . . . . . . . 263
II Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 13 Wave Motion and Waves on a String . . . . . . . . . . . . . 281 14 Sound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 15 Light Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
ix
x
Contents
II I Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 16 Geometrical Optics . . . . . . . . . . . . . . . . . . . . . . . . 371 17 Optical Instruments . . . . . . . . . . . . . . . . . . . . . . . . 435 18 Dispersion and Spectra
. . . . . . . . . . . . . . . . . . . . . 439
19 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 A List List of Physi Physical cal Constan Constants ts . . . . . . . . . . . . . . . . . . . . 446
Part I
Mechanics
θ L
m v
M
1
