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ACING THE GATE WILEY MECHANICAL ENGINEERING ACING THE GATE WILEY MECHANICAL ENGINEERING Ajay Kumar Tamrakar B.E. (GEC, Rewa), M.Tech (IISc) Senior Divisional Mechanical Engineer West Central Railway, Jabalpur, MP Dineshkumar Harursampath B.Tech (IITM), M.E. (IISc), Ph.D. (GeorgiaTech) Assistant Professor and Head, NMCAD Lab Department of Aerospace Engineering Indian Institute of Science, Bangalore ACING THE GATE WILEY MECHANICAL ENGINEERING Copyright © 2014 by Wiley India Pvt. Ltd., 4435-36/7, Ansari Road, Daryaganj, New Delhi-110002. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or scanning without the written permission of the publisher. Limits of Liability: While the publisher and the author have used their best efforts in preparing this book, Wiley and the author make no representation or warranties with respect to the accuracy or completeness of the contents of this book, and specifically disclaim any implied warranties of merchantability or fitness for any particular purpose. There are no warranties which extend beyond the descriptions contained in this paragraph. No warranty may be created or extended by sales representatives or written sales materials. Disclaimer: The contents of this book have been checked for accuracy. Since deviations cannot be precluded entirely, Wiley or its author cannot guarantee full agreement. As the book is intended for educational purpose, Wiley or its author shall not be responsible for any errors, omissions or damages arising out of the use of the information contained in the book. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. Other Wiley Editorial Offices: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030, USA Wiley-VCH Verlag GmbH, Pappellaee 3, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 1 Fusionpolis Walk #07-01 Solaris, South Tower Singapore 138628 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada, M9W 1L1 First Edition: 2014 ISBN: 978-81-265-4542-1 ISBN: 978-81-265-8155-9 (ebk) www.wileyindia.com ✐ ✐ “WileyGateMe” — 2014/2/1 — 11:44 — page v — #5 ✐ ✐ PREFACE The Graduate Aptitude Test in Engineering (GATE) essentially examines the aptitude of an engineering graduate. It differs from other examinations as it calls for an aptitude based learning and approach on engineering topics. However,theaspirantsfacedifficultiesinpreparationforthisexaminationduetovariouscomplications,suchashuge syllabus, unavailability of standard books and trusted texts, existing incongruity with syllabus and approach of the competition, lackofcompetentteachers. Toqualifythisexam, anaspirantshouldhaveperfectunderstandingonthe fundamentals concepts, and requires ability to interpret the fundamental quantities and their relationships. Purpose of this book is to present the subjects of mechanical engineering in a systematic, integrated and precise manner, primarily to meet the requirements of the aspirants of GATE (ME) and to truly help them qualify the examination without unreasonable strains. The book is a self-explanatory and fully-competent text which is equally useful for similar competitions and undergraduate courses in mechanical engineering. The book starts with two introductory articles, “Methodological Concepts in Engineering Studies” and “Strategy for success in GATE”. Each chapter in the manuscript begins with an overview of the content and introduces topics from a level that an average student can follow comfortably. Using easily perceptible language, standard symbols, figures and tables, the book describes various concepts, definitions, and derivations, in a much elucidated text, like a tutor. The book contains almost every mathematical aspect of the subjects with the help of illustrations and by highlighting the implicit path, thus, stimulating curiosity and interest. A summary of important formulas is placed after the theoretical contents in every chapter to provide a quick review of the useful derivations. Solved examples are included to amply demonstrate the theoretical concepts. Each chapter is provided with solutions of previous 11 years’ GATE questions (2003–2013). Each chapter also contains rightly answered and explicitly explained Multiple Choice Questions (MCQ’s) and Numerical Answer Questions (NAQ’s), which are specifically designed to meet the latest pattern and standard of GATE. These questions cover the topics from simplest case and add complexities gradually. The explanations of the questions amply illustrate the topics in a very appealing way. A solved question bank with mixed topics is also placed at the end of the book. Thebookincorporateseverysentenceofimportanceandavoidsundesirablerepetition. Throughoutthecontent,an intuitiveandsystematicapproachisusedtoreinforcethefundamentalunderstandings. Theemphasisonfundamental concepts unveils the inbuilt opportunities for developing the aptitude, the vital element for success in GATE. Despite our best efforts, some errors may have inadvertently crept in the book, we solicit your feedback and suggestions for improvement. Ajay Kumar Tamrakar Dineshkumar Harursampath ✐ ✐ ✐ ✐ ✐ ✐ “WileyGateMe” — 2014/2/1 — 11:44 — page vi — #6 ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ “WileyGateMe” — 2014/2/1 — 11:44 — page vii — #7 ✐ ✐ ACKNOWLEDGMENTS To a mother, who is but a manifestation of the Divine virtues of the Earth, this book is one petite offering. Thank you Amma for being my mother! Thank you Papa for all the liberty, confidence and the discipline showered on me. Thanks to Kiran and Gudiya (my sisters), Amit (my brother), Akash (Kiran’s son) for all the care, love and pride. Thanks to my wife, Deepti, for unflinching support to all my endeavors. Her parents, and Divya, Deepika, Disha (sisters-in-law) own equal gratitude from my side for all their pride for me and for the implicit encouragement. I always seem to get inspiration and renewed vitality by contact with great novel land of my alma mater, Indian Institute of Science, Bangalore, where I enjoyed the privilege of studying with as Dr. Dineshkumar Harursampath, the co-author of this book. It is my proud privilege to express my deep sense of gratitude to him for constant encouragements and invaluable contributions in this book. This project worked as the golden way through which I could return myself to such a venerable teacher. I must also submit my gratitude to Wiley India for considerately accepting the initial proposal of the book which was totally different in pattern and orientation. In spite of busy schedule, Ms. Anjali Chadha and Ms. Sruthi Guru studied the script meticulously and persistently provided support, feedback and inquiries to finally convert the proposal into present book. I am indebted to Mr. Paras Bansal of Wiley India for giving me the opportunity of becoming an author of the publication of such a high repute. Last and not least, I beg forgiveness of all those who have been with me over the course of the years and whose names I have failed to mention. Ajay Kumar Tamrakar ✐ ✐ ✐ ✐ ✐ ✐ “WileyGateMe” — 2014/2/1 — 11:44 — page viii — #8 ✐ ✐ ✐ ✐ ✐ ✐

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Wiley acing the gate mechanical engineering is a self-study book for gate, which is an examination that gauges the aptitude of an engineering student. This examination is different from other aptitude based assessments as here the student has to adopt a more application-based learning and approach t