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CHAPTER ONE UNITS AND MEASUREMENT 1.1 INTRODUCTION Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied ...
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units and abbreviations, developed by the Bureau International des Poids et measures (The International Bureau of Weights and Measures, BIPM) in 1971 were recently revised by the General Conference on Weights and Measures in November 2018. The scheme is now for1.1 Introduction 1.2 The international system of units 1.3 ...
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PHYSICS 2 Table 1.1 SI Base Quantities and Units*international usage in scientific, technical, industrial and commercial work. Because SI units used decimal system, conversions within the system are quite simple and convenient. W e shall follow the SI units in this book. In SI, there are seven base units as given...
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expressed in the unit J s, which is equal to kg m2 s–1, where the metre and the second are defined in terms of c and∆νcs. Time second s The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ∆νcs, the unperturbed ground- state hyperfine transition frequ...
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symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles. Luminous candela cd The candela, symbol cd, is the SI unit of luminous intensity in given direction. intensity It i...
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UNITS AND MEASUREMENT 3 Table 1.2 Some units retained for general use (Though outside SI) Note that when mole is used, the elementary entities must be specified. These entities may be atoms, molecules, ions, electrons, other particles or specified groups of such particles. We employ units for some physical qua...
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say the period of oscillation of a simple pendulum is 1.62 s, the digits 1 and 6 are reliable and certain, while the digit 2 is uncertain. Thus, the measured value has three significant figures. The length of an object reported after measurement to be 287.5 cm has four significant figures, the digits 2, 8, 7 are certai...
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PHYSICS 4 This shows that the location of decimal point is of no consequence in determining the number of significant figures. The example gives the following rules : •All the non-zero digits are significant. •All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all. •I...
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number has two significant figures, while in fact, it has four significant figures and a mere change of units cannot change the number of significant figures. (3) To remove such ambiguities in determining the number of significant figures, the best way is to report every measurement in scientific notation (in the powe...
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The power of 10 is irrelevant to the deter mination of significant figur es. However , all zeroes appearing in the base number in the scientific notation are significant. Each number in this case has four significant figures. Thus, in the scientific notation, no confusion arises about the trailing zero(s) in the base n...
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UNITS AND MEASUREMENT 5 or 2.0000 as required. Similarly, in tTn=, n is an exact number . 1.3.1 Rules for Arithmetic Operations with Significant Figures The result of a calculation involving approximate measured values of quantities (i.e. values with limited number of significant figures) must reflect the uncertainties...
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3.00 × 108 m s-1 (three significant figure) and one year (1y = 365.25 d) has 3.1557 × 107 s (five significant figures), the light year is 9.47 × 1015 m (three significant figures). (2) In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal ...
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figures is 1.75, while the number 1.743 would be 1.74. The rule by convention is that the preceding digit is raised by 1 if the insignificant digit to be dropped (the underlined digit in this case) is more than 5, and is left unchanged if the latter is less than 5 . But what if the number is 2.74 5 in which the ins...
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PHYSICS 6⊳ ⊳of significant figures. The value of π = 3.1415926.... is known to a large number of significant figur es. You may take the value as 3.142 or 3.14 for π, with limited number of significant figures as required in specific cases. Example 1.1 Each side of a cube is measured to be 7.203 m. What are the total...
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the following examples. (1) If the length and breadth of a thin rectangular sheet are measured, using a metre scale as 16.2 cm and, 10.1 cm respectively, there are three significant figures in each measurement. It means that the length l may be written as l = 16.2 ± 0.1 cm = 16.2 cm ± 0.6 ...
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(3) The relative error of a value of number specified to significant figures depends not only on n but also on the number itself. For example, the accuracy in measurement of mass 1.02 g is ± 0.0 1 g whereas another measurement 9.89 g is also accurate to ± 0.0 1 g. The relative error in 1.02 g is = (± 0.01/1.02) × 1...
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UNITS AND MEASUREMENT 7 otherwise rounding errors can build up. For example, the reciprocal of 9.58, calculated (after rounding off) to the same number of significant figures (three) is 0.104, but the reciprocal of 0.104 calculated to three significant figures is 9.62. However , if we had written 1/9.58 = 0.1044 and t...
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and [T]. For example, the volume occupied by an object is expressed as the product of length, breadth and height, or three lengths. Hence the dimensions of volume are [L] × [L] × [L] = [L]3 = [L3]. As the volume is independent of mass and time, it is said to possess zero dimension in mass [M°], zero dimension in time [...
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formula of acceleration and [M L–3 T°] that of mass density. An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. Thus, the dimensional equations are the equations, which represent the dimensions of a physical quantity in terms ...
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PHYSICS 8⊳quantities can be added or subtracted which have the same dimensions. A thorough understanding of dimensional analysis helps us in deducing certain relations among different physical quantities and checking the derivation, accuracy and dimensional consistency or homogeneity of various mathematical expression...
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Dimensions are customarily used as a preliminary test of the consistency of an equation, when there is some doubt about the correctness of the equation. However , the dimensional consistency does not guarantee correct equations. It is uncertain to the extent of dimensionless quantities or functions. The arguments of sp...
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test of consistency of units, but has the advantage that we need not commit ourselves to a particular choice of units, and we need not worry about conversions among multiples and sub-multiples of the units. It may be borne in mind that if an equation fails this consistency test, it is proved wrong, but if it passes, i...
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UNITS AND MEASUREMENT 9⊳⊳The dimensions of RHS are [M][L T–2] [L] = [M][L2 T–2] = [M L2 T–2] The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct. ⊳ Example 1.4 The SI unit of energy is J = kg m2 s–2; that of speed v is m s–1 and of acceleration a is m s–...
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cannot tell which of the two, (b) or (d), is the correct formula. For this, one must turn to the actual definition of kinetic energy (see Chapter 5). The correct formula for kinetic energy is given by (b). ⊳ 1.6.2 Deducing Relation among the Physical Quantities The method of dimensions can sometimes be used to deduce...
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So that 1 1, – , 02 2x y z= = = Then, T = k l½ g–½ or, T = lkg Note that value of constant k can not be obtained by the method of dimensions. Here it does not matter if some number multiplies the right side of this formula, because that does not affect its dimensions. Actually, k = 2π so that T = 2l gπ ⊳ Dimensional an...
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PHYSICS 10 SUMMARY 1.Physics is a quantitative science, based on measurement of physical quantities. Certain physical quantities have been chosen as fundamental or base quantities (such as length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity). 2.Each base quantit...
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expressing properly the physical quantities and measurements. 9.In computing any physical quantity, the units for derived quantities involved in the relationship(s) are treated as though they were algebraic quantities till the desired units are obtained. 10.In measured and computed quantities proper significant figures...
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(c) 3.0 m s–2 = .... km h–2 (d) G = 6.67 × 10–11 N m2 (kg)–2 = .... (cm)3 s–2 g–1. Rationalised-2023-24
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UNITS AND MEASUREMENT 11 1.3 A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J = 1 kg m2 s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α–1 β–2 γ2 in terms ...
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microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair ? 1.8 Answer the following : (a)You ar e given a thr ead and a metr e scale. How will you estimate the diameter of the t...
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2.01 cm respectively. Give the area and volume of the sheet to correct significant figures. 1.12 The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is (a) the total mass of the box, (b) the difference in the masses of the pieces to cor...
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PHYSICS 12 1.14 The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å: 1 Å = 10–10 m. The size of a hydrogen atom is about 0.5 Å. What is the total atomic volume in m3 of a mole of hydrogen atoms ? 1.15 One mole of an ideal gas at standard temperature and pressure occupies 22.4 ...
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C KC K PART I TEXTBOOK FOR CLASS XI Rationalised-2023-24
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C K C KFirst Edition February 2006 Phalguna 1927 Reprinted October 2006 Kartika 1928 December 2007 Pausa 1929 January 2009 Pausa 1930 January 2010 Pausa 1931 January 2011 Pausa 1932 March 2012 Phalguna 1933 November 2012 Kartika 1934 PD 350T RNB © National Council of Educational Research and Training, 2006 ` `` `` 1...
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DIVISION, NCERT NCERT Campus Sri Aurobindo Marg New Delhi 110 016 Phone : 011-26562708 108, 100 Feet Road Hosdakere Halli Extension Banashankari III Stage Bangalore 560 085 Phone : 080-26725740 Navjivan Trust Building P.O.Navjivan Ahmedabad 380 014 Phone : 079-27541446 CWC Campus Opp. Dhankal Bus Stop Panihati Kolka...
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qNo part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. qThis book is sold subject to the condition that it shall not, by way of trade, be lent, ...
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December 2014, May 2016, February 2017, December 2017, January 2019, October 2019, January 2021, July 2021 and November 2021 Revised Edition November 2022 Kartika 1944 PD 400T BS © National Council of Educational Research and Training, 2006, 2022 ` `` `` 150.00 Printed on 80 GSM paper with NCER T watermark Published at...
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qNo part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. qThis book is sold subject to the condition that it shall not, by way of trade, be lent, ...
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Production Assistant :Om Prakash Cover and Illustrations Shweta Rao11086 – P HYSICS (PART I) Textbook for Class XIISBN 81-7450-508-3 Rationalised-2023-24
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C KC K FOREWORD The National Curriculum Framework (NCF), 2005 recommends that children’s life at school must be linked to their life outside the school. This principle marks a departure from the legacy of bookish learning which continues to shape our system and causes a gap between the school, home and community. The ...
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the problem of curricular burden by restructuring and reorienting knowledge at different stages with greater consideration for child psychology and the time available for teaching. The textbook attempts to enhance this endeavour by giving higher priority and space to opportunities for contemplation and wondering, discu...
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C K C K Rationalised-2023-24
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C KC K RATIONALISATION OF CONTENT IN THE TEXTBOOKS In view of the COVID-19 pandemic, it is imperative to reduce content load on students. The National Education Policy 2020, also emphasises reducing the content load and providing opportunities for experiential learning with cr eative mindset. In this backgr ound, the...
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C K C K Rationalised-2023-24
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C KC K TEXTBOOK D EVELOPMENT COMMITTEE CHAIRPERSON , ADVISORY GROUP FOR TEXTBOOKS IN SCIENCE AND MATHEMATICS J.V. Narlikar , Emeritus Pr ofessor , Chair man, Advisory Committee , Inter University Centre for Astronomy and Astrophysics (IUC AA), Ganesh khind, Pune University, Pune CHIEF ADVISOR A.W. Joshi, Professor...
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S. Rai Choudhary, Pr ofessor , Department of Physics and Astr ophysics, University of Delhi, Delhi S.K. Dash, Reader , DESM, NCER T, New Delhi Sher Singh, PGT, NDMC Navyug School, Lodhi Road, New Delhi S.N. Prabhakara, PGT, DM School, Regional Institute of Education, NCER T, Mysor e Thiyam Jekendra Singh, Professor ,...
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C K C KACKNOWLEDGEMENTS The National Council of Educational Resear ch and T raining acknowledges the valuable contribution of the individuals and organisations involved in the development of Physics textbook for Class XI. The Council also acknowledges the valuable contribution of the following academics for reviewing a...
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PGT, Vasant V alley School, V asant Kunj, New Delhi; R.S. Dass, Vice Principal (Retd), Balwant Ray Mehta V idya Bhawan, Lajpat Nagar , New Delhi and Parthasarthi Panigrahi, PGT, D.V. CLW Girls School, Chittranjan, W est Bengal. The Council also gratefully acknowledges the valuable contribution of the following academic...
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for her support. The Council also acknowledges the ef forts of Deepak Kapoor , Inchar ge, Computer Station, Inder Kumar , DTP Operator ; Saswati Banerjee, Copy Editor; Abhimanu Mohanty and Anuradha, Proof Readers in shaping this book. The contributions of the Publication Department in bringing out this book are also d...
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C KC K PREFACE More than a decade ago, based on National Policy of Education (NPE-1986), National Council of Educational Research and Training published physics textbooks for Classes XI and XII, prepared under the chairmanship of Professor T . V. Ramakrishnan, F .R.S., with the help of a team of lear ned co-authors. Th...
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process of physics useful in any other branch they may like to pursue, be it finance, administration, social sciences, environment, engineering, technology, biology or medicine. For those who pursue physics beyond this stage, the matter developed in these books will certainly provide a sound base. Physics is basic to t...
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common English or Latin or Greek, but gives entirely different meanings to these words. It would be illuminating to look up wor ds like ener gy, for ce, power , char ge, spin, and several others, in any standard English dictionary, and compare their Rationalised-2023-24
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C K C Kx meanings with their physics meanings. Physics develops intricate and often weird- looking concepts to explain the behaviour of particles. Finally, it must be remembered that entire physics is based on observations and experiments, without which a theory does not get acceptance into the domain of physics. This ...
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have included the necessary tools and database in the form of Appendices A-1 to A-9 at the end of the book. There are also some other appendices at the end of some chapters giving additional information or applications of matter discussed in that chapter . Special attention has been paid for providing illustrative fig...
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on acquiring pr ofessional competence, in some chosen fields of endeavour . You may like to compare this with the following situation. Children play cricket or badminton in lanes and small spaces outside (or inside) their homes. But then Rationalised-2023-24
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C KC K some of them want to make it to the school team, then district team, then State team and then the National team. At every stage, there is bound to be a steep gradient. Hard work would have to be put in whether students want to pursue their education in the area of sciences, humanities, languages, music, fine art...
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Occasionally, substantial portions from the earlier versions, particularly those appreciated by students/teachers, have been adopted/adapted and retained in the present book for the benefit of coming generation of learners. We welcome suggestions and comments fr om our valued users, especially students and teachers. W ...
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C K C KA NOTE FOR THE TEACHERS To make the curriculum lear ner-centr ed, students should be made to participate and interact in the learning process directly. Once a week or one out of every six classes would be a good periodicity for such seminars and mutual interaction. Some suggestions for making the discussion part...
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Write down what message each one of you would like to leave for future generations. Then discuss it in your group and add or modify, if you want to change your mind. Give it to your teacher and join in any discussion that follows. 2.Reductionism Kinetic Theory of Gases relates the Big to the Small, the Macro to the Mic...
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in both. Give reasons. Write down your answers. Discuss with the group and modify them or add comments. Give to the teacher and join in the discussion. Students and teachers will find that such seminars and discussions lead to tremendous understanding, not only of physics, but also of science and social sciences. They ...
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C KC K CONTENTS FOREWORD iii RATIONALISATION OF CONTENT IN THE TEXTBOOKS v PREFACE ix A N OTE FOR THE TEACHER xii C H A P T E R 1 UNITS AND MEASUREMENTS 1.1 Introduction 1 1.2 The international system of units 1 1.3 Significant figures 3 1.4 Dimensions of physical quantities 7 1.5 Dimensional formulae and dimensio...
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C K C K4.7 Conservation of momentum 57 4.8 Equilibrium of a particle 58 4.9 Common forces in mechanics 59 4.10 Circular motion 63 4.11 Solving problems in mechanics 64 C H A P T E R 5 WORK, ENERGY AND POWER 5.1 Introduction 71 5.2 Notions of work and kinetic energy : The work-energy theorem 73 5.3 Work 73 5.4 Kineti...
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7.2 Kepler’s laws 128 7.3 Universal law of gravitation 129 7.4 The gravitational constant 131 7.5 Acceleration due to gravity of the earth 132 7.6 Acceleration due to gravity below and above the surface of earth 133xiv Rationalised-2023-24
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C KC K 7.7 Gravitational potential energy 134 7.8 Escape speed 135 7.9 Earth satellites 137 7.10 Energy of an orbiting satellite 138 APPENDICES 144 ANSWERS 160xv Rationalised-2023-24
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C K C KCOVER DESIGN (Adapted from the website of the Nobel Foundation http://www.nobelprize.org) The strong nuclear force binds protons and neutrons in a nucleus and is the strongest of nature’s four fundamental forces. A mystery surrounding the strong nuclear force has been solved. The three quarks within the proton c...
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