Understanding Physics JEE Main & Advanced MECHANICS Volume 1 Understanding Physics JEE Main & Advanced MECHANICS Volume 1 DC PANDEY [B.Tech, M.Tech, Pantnagar, ID 15722] ARIHANT PRAKASHAN (Series), MEERUT Understanding Physics JEE Main & Advanced ARIHANT PRAKASHAN (Series), MEERUT All Rights Reserved © SARITA PANDEY No part of this publication may be re-produced, stored in a retrieval system or by any means, electronic, mechanical, photocopying, recording, scanning, web or otherwise without the written permission of the publisher. Arihant has obtained all the information in this book from the sources believed to be reliable and true. However, Arihant or its editors or authors or illustrators don’t take any responsibility for the absolute accuracy of any information published and the damage or loss suffered thereupon. All disputes subject to Meerut (UP) jurisdiction only. ADMINISTRATIVE & PRODUCTION OFFICES Regd. Office 'Ramchhaya' 4577/15, Agarwal Road, Darya Ganj, New Delhi -110002 Tele: 011- 47630600, 43518550; Fax: 011- 23280316 Head Office Kalindi, TP Nagar, Meerut (UP) - 250002 Tel: 0121-2401479, 2512970, 4004199; Fax: 0121-2401648 SALES & SUPPORT OFFICES Agra, Ahmedabad, Bengaluru, Bareilly, Chennai, Delhi, Guwahati, Hyderabad, Jaipur, Jhansi, Kolkata, Lucknow, Meerut, Nagpur & Pune. ISBN 978-93-13190-55-4 Published by ARIHANT PUBLICATIONS (I) LTD. For further information about the books published by Arihant, log on to www.arihantbooks.com or e-mail at [email protected] /arihantpub /@arihantpub Arihant Publications /arihantpub Understanding Physics JEE Main & Advanced PREFACE The overwhelming response to the previous editions of this book gives me an immense feeling of satisfaction and I take this an opportunity to thank all the teachers and the whole student community who have found this book really beneficial. In the present scenario of ever-changing syllabus and the test pattern of JEE Main & Advanced. The NEW EDITION of this book is an effort to cater all the difficulties being faced by the students during their preparation of JEE Main & Advanced. Almost all types and levels of questions are included in this book. My aim is to present the students a fully comprehensive textbook which will help and guide them for all types of examinations. An attempt has been made to remove all the printing errors that had crept in the previous editions. I am very thankful to (Dr.) Mrs. Sarita Pandey, Mr. Anoop Dhyani and Mr. Nisar Ahmad Comments and criticism from readers will be highly appreciated and incorporated in the subsequent editions. DC Pandey Understanding Physics JEE Main & Advanced CONTENTS 1. BASIC MATHEMATICS 1-12 1.1 Basic Mathematics 2. MEASUREMENT AND ERRORS 13-31 2.1 Errors in Measurement and Least Count 2.2 Significant Figures 2.3 Rounding off a Digit 2.4 Algebraic Operations with Significant Figures 2.5 Error Analysis 3. EXPERIMENTS 33-78 3.1 Vernier Callipers 3.2 Screw Gauge 3.3 Determination of ‘g’ using a Simple Pendulum 3.4 Young’s Modulus by Searle’s Method 3.5 Determination of Specific Heat 3.6 Speed of Sound using Resonance Tube 3.7 Verification of Ohm’s Law using Voltmeter and Ammeter 3.8 Meter Bridge Experiment 3.9 Post Office Box 3.10 Focal Length of a Concave Mirror using u-v method 3.11 Focal Length of a Convex Lens using u-v method Understanding Physics JEE Main & Advanced 4. UNITS AND DIMENSIONS 79-96 4.1 Units 4.2 Fundamental and Derived Units 4.3 Dimensions 4.4 Uses of Dimensions 5. VECTORS 97-125 5.1 Vector and Scalar Quantities 5.2 General Points regarding Vectors 5.3 Addition and Subtraction of Two Vectors 5.4 Components of a Vector 5.5 Product of Two Vectors 6. KINEMATICS 127-214 6.1 Introduction to Mechanics and Kinematics 6.2 Few General Points of Motion 6.3 Classification of Motion 6.4 Basic Definition 6.5 Uniform Motion 6.6 One Dimensional Motion with Uniform Acceleration 6.7 One Dimensional Motion with Non-uniform Acceleration 6.8 Motion in Two and Three Dimensions 6.9 Graphs 6.10 Relative Motion 7. PROJECTILE MOTION 215-259 7.1 Introduction 7.2 Projectile Motion 7.3 Two Methods of Solving a Projectile Motion 7.4 Time of Flight, Maximum Height and Horizontal Range of a Projectile 7.5 Projectile Motion along an Inclined Plane 7.6 Relative Motion between Two Projectiles Understanding Physics JEE Main & Advanced 8. LAWS OF MOTION 261-359 8.1 Types of Forces 8.2 Free Body Diagram 8.3 Equilibrium 8.4 Newton’s Laws of Motion 8.5 Constraint Equations 8.6 Pseudo Force 8.7 Friction 9. WORK, ENERGY AND POWER 361-427 9.1 Introduction to Work 9.2 Work Done 9.3 Conservative and Non-conservative Forces 9.4 Kinetic Energy 9.5 Work-Energy Theorem 9.6 Potential Energy 9.7 Three Types of Equilibrium 9.8 Power of a Force 9.9 Law of Conservation of Mechanical Energy 10. CIRCULAR MOTION 429-476 10.1 Introduction 10.2 Kinematics of Circular Motion 10.3 Dynamics of Circular Motion 10.4 Centrifugal Force 10.5 Motion in a Vertical Circle Hints & Solutions 477-608 JEE Main & Advanced Previous Years' Questions (2018-13) 1-18 Understanding Physics JEE Main & Advanced SYLLABUS JEE M ain Physics and M easurement Physics, Technology and Society, SI units, Fundamental and derived units, Least count, Accuracy and Precision of measuring instruments, Errors in measurement, Dimensions of physical quantities, Dimensional analysis and its applications. Kinematics Frame of reference, Motion in a straight line, Position-time graph, Speed and velocity, Uniform and non-uniform motion, Average speed and instantaneous velocity, Uniformly accelerated motion, Velocity-time and position-time graphs, Relations for uniformly accelerated motion, Scalars and Vectors, vectors addition and subtraction, Zero vector, scalar and vector products, Unit vector, resolution of a vector, Relative velocity, motion in plane, Projectile motion, Uniform circular motion. Laws o f M otion Force and inertia, Newton's first law of motion, Momentum, Newton's second law of motion, impulse, Newton's third Law of motion, law of conservation of linear momentum and its applications, Equilibrium of concurrent forces. Static and kinetic friction, Laws of friction, rolling friction. Dynamics of uniform circular motion, centripetal force and its applications. Work, Energy a nd P ower Work done by a constant force and a variable force, Kinetic and potential energies, Work energy theorem, power. Potential energy of a spring, Conservation of mechanical energy, Conservative and non-conservative forces, Elastic and inelastic collisions in one and two dimensions. Centre of Mass Centre of mass of a two particle system, Centre of mass of a rigid body. Experimental Skills Vernier Callipers and its use to measure internal and external diameter and depth of a vessel. Screw gauge its use to determine thickness/diameter of thin sheet/wire. Understanding Physics JEE Main & Advanced JEE A dvanced General Physics Units and dimensions, Dimensional analysis, Least count, Significant figures, Methods of measurement and error analysis for physical quantities pertaining to the following experiments, Experiments based on vernier callipers and screw gauge (micrometer). Kinematics Kinematics in one and two dimensions (Cartesian coordinates only), Projectiles, Uniform circular motion, Relative velocity. Laws of Motion Newton's laws of motion, Inertial and uniformly accelerated frames of reference, Static and dynamic friction. Work, Energy and Power Kinetic and potential energy, Work and power, Conservation of linear momentum and mechanical energy. Centre of Mass and Collision System of particles, Centre of mass and its motion, Impulse, Elastic and inelastic collisions.