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- Numerical relativity - Reconstructed (template) '.§:0.6 " i Z, 0.5 - Black hole separation...

- Numerical relativity - Reconstructed (template) '.§:0.6 " i Z, 0.5 - Black hole separation I --...... 3 C: 0 0.4 - Black hole relative velocity I 2 15 0.3 1 !g_ 0.30 0.35 0.40 0.45 0 Time (s) Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune. The Coordination Committee formed by GR No. Abhyas - 2116/(Pra.Kra.43/16) SD - 4 Dated 25.4.2016 has given approval to prescribe this textbook in its meeting held on 20.06.2019 and it has been decided to implement it from academic year 2019-20. PHYSICS Standard XI Download DIKSHA App on your smartphone. If you scan the Q.R.Code on this page of your textbook, you will be able to access full text. If you scan the Q.R.Code provided, you will be able to access audio-visual study material relevant to each lesson, provided as teaching and learning aids. 2019 Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune. First Edition : © Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune - 411 004. 2019 The Maharashtra State Bureau of Textbook Production and Curriculum Reprint: 2020 Research reserves all rights relating to the book. No part of this book should be reproduced without the written permission of the Director, Maharashtra State Bureau of Textbook Production and Curriculum Research, ‘Balbharati’, Senapati Bapat Marg, Pune 411004. Illustration Subject Committee: Shri. Pradeep Ghodke Dr. Chandrashekhar V. Murumkar, Chairman Shri. Shubham Chavan Dr. Dilip Sadashiv Joag, Member Cover Dr. Pushpa Avinash Khare, Member Shri. Vivekanand S. Patil Dr. Rajendra Shankar Mahamuni, Member Typesetting Dr. Anjali Lalit Kshirsagar, Member DTP Section, Textbook Bureau, Dr. Rishi Baboo Sharma , Member Pune Shri. Rajiv Arun Patole, Member Secretary Co-ordination : Shri. Rajiv Arun Patole Study group: Special Officer for Physics Dr. Umesh Anant Palnitkar Dr. Vandana Laxmanrao Jadhav Patil Paper : Dr. Neelam Sunil Shinde 70 GSM Creamwove Dr. Radhika Gautamkumar Deshmukh Print Order : Dr. Prabhakar Nagnath Kshirsagar Dr. Bari Anil Ramdas Dr. Sutar Milind Madhusudan Printer Dr. Bodade Archana Balasaheb Dr. Chavan Jayashri Kalyanrao Smt. Chokshi Falguni Manish Production : Shri. Ramesh Devidas Deshpande Shri Sachchitanand Aphale Shri. Vinayak Shripad Katdare Chief Production Officer Smt. Pratibha Pradeep Pandit Shri. Dinesh Madhusudan Joshi Shri Liladhar Atram Shri. Kolase Prashant Panditrao Production Officer Shri. Brijesh Pandey Shri. Ramchandra Sambhaji Shinde Publisher : Smt. Taksale Mugdha Milind Shri Vivek Uttam Gosavi Controller Maharashtra State Textbook Smt. Prachi Ravindra Sathe Bureau, Prabhadevi, Chief Co-ordinator Mumbai - 400 025 The Constitution of India Preamble WE, THE PEOPLE OF INDIA, having solemnly resolved to constitute India into a SOVEREIGN SOCIALIST SECULAR DEMOCRATIC REPUBLIC and to secure to all its citizens: JUSTICE, social, economic and political; LIBERTY of thought, expression, belief, faith and worship; EQUALITY of status and    of opportunity; and to promote among them all FRATERNITY assuring the dignity of the individual and the unity and integrity of the Nation; IN OUR CONSTITUENT ASSEMBLY this twenty-sixth day of November, 1949, do HEREBY ADOPT, ENACT AND GIVE TO OURSELVES THIS CONSTITUTION. NATIONAL ANTHEM Preface Dear Students, It is a matter of pleasure and pride to place this exposition on basic physics in the hands of the young generation. This is not only textbook of physics for standard XI class , but embodies material which will be useful for self-study. This textbook aims to create awareness about Physics. The National Curriculum Framework (NCF) was formulated in the year 2005, followed by the State Curriculum Framework (SCF) in 2010. Based on the given two frameworks, reconstruction of the curriculum and preparation of a revised syllabus has been undertaken which will be introduced from the academic year 2019-20. The textbook incorporating the revised syllabus has been prepared and designed by the Maharashtra State Bureau of Textbook Production and Curriculum Research, (Balbharati), Pune. The purpose of the book is to prepare a solid foundation for further studies in physics at the standard XII class. Proficiency in science in general and physics in particular is a basic requirement for the professional courses such as engineering and medicine etc., apart from the graduation courses in science itself. With this point of view , each chapter is prepared with elementary level and encompassing the secondary school level physics to the higher secondary level. Most of the topics are explained lucidly and in sufficient details, so that the students understand them well. A number of illustrative examples and figures are included to enlighten the student proficiency.With this background, the student is expected to solve the exercises given at the end of the chapters. For students who want more, Internet sites for many topics have been provided. They can enjoy further reading. After all, physics is a conceptual subject. Knowledge about physical phenomena is gained as a natural consequence of observation, experience and revelation upon problem solving. The book is written with this mind-set. The curriculum and syllabus conforms to the maxims of teaching such as moving from concrete to abstract, known to unknown and from part to the whole. For the first time, in this textbook of Physics, various activities have been introduced. These activities will not only help to develop understanding the content but also provide scope of the for gaining relevant and additional knowledge on your own efforts. A detailed information of all concepts is also given for a better understanding of the subject. QR Codes have been introduced for gaining additional information, abstracts of chapters and practice questions/ activities. The efforts taken to prepare the textbook will not only enrich the learning experiences of the students, but also benefit other stakeholders such as teachers, parents as well as candidates aspiring for the competitive examinations. We look forward to a positive response from the teachers and students. Our best wishes to all! Pune (Dr. Sunil Magar) Date : 20 June 2019 Director Maharashtra State Bureau of Bhartiya Saur : 30 Jyeshtha 1941 Textbook Production and Curriculum Research, Pune 4 - For Teachers - Dear Teachers, P 'Error in measurements' is an important We are happy to introduce the revised topic in physics. Please ask the students to textbook of Physics for Std XI. This book use this in estimating errors in their is a sincere attempt to follow the maxims measurements. This must become an of teaching as well as develop a integral part of laboratory practices. ‘constructivist’ approach to enhance the P Major concepts of physics have a scientific quality of learning. The demand for more base. Encourage group work, learning activity based, experiential and innovative through each other’s help etc. Facilitate learning opportunities is the need of the peer learning as much as possible by hour. The present curriculum has been reorganizing the class structure frequently. restructured so as to bridge the credibility P Do not use the boxes titled ‘Do you know?’ gap that exists between what is taught and for evaluation. However, teachers must what students learn from direct experience ensure that students read this extra in the outside world. Guidelines provided information. below will help to enrich the teaching- P For evaluation, equal weightage should be learning process and achieve the desired assigned to all the topics. Use different learning outcomes. combinations of questions. Stereotype P To begin with, get familiar with the questions should be avoided. textbook yourself, and encourage the P Use QR Code given in the textbook. Keep students to read each chapter carefully. checking the QR Code for updated P The present book has been prepared for information. Certain important links, websites constructivist and activity-based teaching, have been given for references. Also a list including problem solving exercises. of reference books is given. Teachers as well P Use teaching aids as required for proper as the students can use these references for understanding of the subject. extra reading and in-depth understanding of P Do not finish the chapter in short. the subject. P Follow the order of the chapters strictly as Best wishes for a wonderful teaching listed in the contents because the units are experience! introduced in a graded manner to facilitate knowledge building. References: 1. Fundamentals of Physics - Halliday, Resnick, Walker; John Wiley (sixth ed.). 2. Sears and Zeemansky's University Physics - Young and Freedman, Pearson Education (12th ed.) 3. Physics for Scientists and Engineers - Lawrence S. Lerner; Jones and Bartlett Publishers, UK. Front Page : Figure shows the LIGO laboratory in the United States of America and the inset shows the trace of gravity waves detected upon the merger of two black holes. In the background is the artist's impression of planets and galaxies. Since ages, mankind is awed by the sheer scale of the universe and is trying to understand the laws governing the same. Today we observe the events in the universe with highly sophisticated instruments and laboratories such as the LIGO project seen on the cover. Picture Credit: Caltech/ MIT/ LIGO laboratory. Figure Credit : B. P. Abott et al. Physical Review letts 116, 061102, 2016 DISCLAIMER Note : All attempts have been made to contact copy right/s (©) but we have not heard from them. We will be pleased to acknowledge the copy right holder (s) in our next edition if we learn from them. Competency Statements Standard XI Area/ Unit/ Competency Statements Lesson After studying the content in Textbook student … Units and Distinguish between fundamental and derived quantities. Mathematical Distinguish between different system of units and their use. Tools Identify methods to be used for measuring lengths and distances of varying magnitudes. Check correctness of physical equations using dimensional analysis. Establish the relation between related physical quantities using dimensional analysis. Find conversion factors between the units of the same physical quantity in two different sets of units. Identify different types of errors in measurement of physical quantities and estimate them. Identify the order of magnitude of a given quantity and the significant figures in them. Distinguish between scalar and vector quantities. Perform addition, subtraction and multiplication (scalar and vector product) of vectors. Determine the relative velocity between two objects. Obtain derivatives and integrals of simple functions. Obtain components of vectors. Apply mathematical tools to analyze physics problems. Motion and Visualize motions in daily life in one, two and three dimensions. Gravitation Explain the necessity of Newton’s first law of motion. Categorize various forces of nature into four fundamental forces. State various conservation principles and use these in daily life situations. Derive expressions and evaluate work done by a constant force and variable force. Organize/categorize the common principles between collisions and explosions. Explain the necessity of defining impulse and apply it to collisions, etc. Elaborate the limitations of Newton’s laws of motion. Elaborate different types of mechanical equilibria with suitable examples. Apply the Kepler’s laws of planetary motion to solar system. Elaborate Newton’s law of gravitation. Calculate the values of acceleration due to gravity at any height above and depth below the earth’s surface. Distinguish between different orbits of earth’s satellite. Explain how escape velocity varies from planet. Explain weightlessness in a satellite. Properties of Explain the difference between elasticity and plasticity Matter Identify elastic limit for a given material. Differentiate between different types of elasticity modules. Judge the suitability of materials for specific applications in daily life appliances. Identify the role of force of friction in daily life. Differentiate between good and bad conductors of heat. Relate underlying physics for use of specific materials for use in thermometers for specific applications. Sound and Optics Apply and relate various parameters related to wave motion. Compare various types of waves with common features and distinguishing features. Analytically relate the factors on which the speed of sound and speed of light depends. Explain the essential factor to describe wave propagation and relate it with phase angle. Apply the laws of reflection to light. Mathematically describe the Doppler effect for sound waves. Apply the laws of refraction to common phenomena in daily life like, a mirage or a rainbow. Identify the defects in images obtained by mirrors and lenses, with their cause and ways of reducing or eliminating them. Explain the construction and use of various optical instruments such as a microscope, a telescope, etc. Relate dispersion of light with colour and apply it analytically with the help of prisms. Describe dispersive power as a basic property of transparent materials and relate it with their refractive indices. Analyze the time taken to receive an echo and calculate distance to the reflecting object. Explain reverberation and acoustics. Electricity and Distinguish between conductors and insulators. Magnetism Apply coulomb’s law and obtain the electric field due to a certain distribution of charges. Define dipole, obtain the dipolar field. Relate the drift of electrons in a conductor to resistivity Calculate resistivity at various temperature. Connect resistors in series and parallel combination. Compare electric and magnetic fields. Draw electric and magnetic lines of force. Obtain magnetic parameters of the Earth. Solve numerical and analytical problems. Communication Explain the properties of an electromagnetic wave. and Distinguish between mechanical waves and electromagnetic waves. Semiconductors Identify different types of electromagnetic radiations from γ- rays to radio waves. Distinguish between different modes of propagation of EM waves through earth’s atmosphere. Identify different elements of a communication system. Explain different types of modulation and identify the types of modulation needed in given situation. Distinguish between conductors, insulators and semiconductors based on band structure. Differentiate between p type and n type semiconductors and their uses. Explain working of forward and reverse biased junction. Explain the working of semiconductor diode. CONTENTS Sr. No Title Page No 1 Units and Measurements 1-15 2 Mathematical Methods 16-29 3 Motion in a Plane 30-46 4 Laws of Motion 47-77 5 Gravitation 78-99 6 Mechanical Properties of Solids 100-113 7 Thermal Properties of Matter 114-141 8 Sound 142-158 9 Optics 159-187 10 Electrostatics 188-206 11 Electric Current Through Conductors 207-220 12 Magnetism 221-228 13 Electromagnetic Waves and Communication System 229-241 14 Semiconductors 242-256 1. Units and Measurements Can you recall? 1. What is a unit? 2. Which units have you used in the laboratory for measuring (i) length (ii) mass (iii) time (iv) temperature? 3. Which system of units have you used? 1.1 Introduction: 1.2.1 Fundamental Quantities and Units: Physics is a quantitative science, where The physical quantities which do not we measure various physical quantities depend on any other physical quantities for during experiments. In our day to day life, we their measurements are known as fundamental need to measure a number of quantities, e.g., quantities. There are seven fundamental size of objects, volume of liquids, amount of quantities: length, mass, time, temperature, matter, weight of vegetables or fruits, body electric current, luminous intensity and amount temperature, length of cloth, etc. A measurement of substance. always involves a comparison with a standard Fundamental units: The units used to measure measuring unit which is internationally fundamental quantities are called fundamental accepted. For example, for measuring the mass units. The fundamental quantities, their units of a given fruit we need standard mass units and symbols are shown in the Table 1.1. of 1 kg, 500 g, etc. These standards are called Table 1.1: Fundamental Quantities with units. The measured quantity is expressed in their SI Units and Symbols terms of a number followed by a corresponding unit, e.g., the length of a wire is written as 5 m Fundamental quantity SI units Symbol where m (metre) is the unit and 5 is the value of 1) Length metre m the length in that unit. Different quantities are 2) Mass kilogram kg measured in different units, e.g. length in metre 3) Time second s (m), time in seconds (s), mass in kilogram (kg), 4) Temperature kelvin K etc. The standard measure of any quantity is 5) Electric current ampere A called the unit of that quantity. 6) Luminous Intensity candela cd 1.2 System of Units: 7) Amount of substance mole mol In our earlier standards we have come 1.2.2 Derived Quantities and Units: across various systems of units namely In physics, we come across a large number (i) CGS: Centimetre Gram Second system of quantities like speed, momentum, resistance, (ii) MKS: Metre Kilogram Second system conductivity, etc. which depend on some or all (iii) FPS: Foot Pound Second system. of the seven fundamental quantities and can be (iv) SI: System International expressed in terms of these quantities. These are called derived quantities and their units, which The first three systems namely CGS, MKS can be expressed in terms of the fundamental and FPS were used extensively till recently. In units, are called derived units. 1971, the 14th International general conference on weights and measures recommended the For example, use of ‘International system' of units. This SI unit of velocity international system of units is called the Unit of displacement m SI units. As the SI units use decimal system,    m s 1 Unit of time s conversion within the system is very simple and Unit of momentum = (Unit of mass)×(Unit of convenient. velocity) 1 = kg m/s = kg m s-1 Area of the disc of the moon The above two units are derived units. = (moon - earth distance) 2 Supplementary units : Besides, the seven  × (1.737×103 ) 2 fundamental or basic units, there are two more = (3.84 ×105 ) 2 units called supplementary units: (i) Plane angle dθ and (ii) Solid angle dΩ = 6.425  10-5 sr (i) Plane angle (dθ) : This is the ratio of the Do you know ? length of an arc of a circle to the radius of The relation between radian and degree is the circle as shown in Fig. 1.1 (a). Thus π radians = πc = 180° dθ = ds/r is the angle subtended by the arc at the centre of the circle. It is measured in radian (rad). An angle θ in radian is denoted as θc. (ii) Solid angle (dΩ) : This is the 3-dimensional analogue of dθ and is defined as the area of a portion of surface of a sphere to 1.2.3 Conventions for the use of SI Units: the square of radius of the sphere. Thus (1) Unit of every physical quantity should be dΩ = dA/r2 is the solid angle subtended by represented by its symbol. area ds at O as shown in Fig. 1.1 (b). It (2) Full name of a unit always starts with is measured in steradians (sr). A sphere of smaller letter even if the name is after a radius r has surface area 4πr2. Thus, the person, e.g., 1 newton, 1 joule, etc. But solid angle subtended by the entire sphere symbol for unit named after a person at its centre is Ω = 4πr2/r2 = 4π sr. should be in capital letter, e.g., N after A scientist Newton, J after scientist Joule, etc. ds (3) Symbols for units do not take plural form dθ for example, force of 20 N and not 20 O r B newtons or not 20 Ns. Fig 1.1 (a): Plane angle dθ. (4) Symbols for units do not contain any full stops at the end of recommended letter, e.g., 25 kg and not 25 kg.. dA (5) The units of physical quantities in numerator and denominator should be written as one ratio for example the SI r unit of acceleration is m/s2 or m s-2 but not m/s/s. (6) Use of combination of units and symbols for units is avoided when physical O quantity is expressed by combination of Fig 1.1 (b): Solid angle dΩ. two. e.g., The unit J/kg K is correct while joule/kg K is not correct. Example 1.1: What is the solid angle subtended (7) A prefix symbol is used before the symbol by the moon at any point of the Earth, given of the unit. the diameter of the moon is 3474 km and its Thus prefix symbol and units symbol distance from the Earth 3.84×108 m. constitute a new symbol for the unit which Solution: Solid angle subtended by the moon can be raised to a positive or negative at the Earth power of 10. 2 1ms = 1 millisecond = 10-3s discussed earlier is length. To measure the 1µs = 1 microsecond = 10-6s length or distance the SI unit used is metre 1ns = 1 nanosecond = 10-9s (m). In 1960, a standard for the metre based Use of double prefixes is avoided when on the wavelength of orange-red light emitted single prefix is available by atoms of krypton was adopted. By 1983 a 10-6s =1µs and not 1mms. more precise measurement was developed. 10-9s = 1ns and not 1mµs It says that a metre is the length of the path (8) Space or hyphen must be introduced travelled by light in vacuum during a time while indicating multiplication of two interval of 1/299792458 second. This was units e.g., m/s should be written as m s-1 possible as by that time the speed of light or m-s-1 and Not as ms-1 (because ms will in vacuum could be measured precisely as be read as millisecond). c = 299792458 m/s 1.3 Measurement of Length: Some typical distances/lengths are given in One fundamental quantity which we have Table 1.2. Table 1.2: Some Useful Distances Measurement Length in metre Distance to Andromeda Galaxy (from Earth) 2×1022 m Distance to nearest star (after Sun) Proxima Centuari (from Earth) 4×1016 m Distance to Pluto (from Earth) 6×1012 m Average Radius of Earth 6×106 m Height of Mount Everest 9×103 m Thickness of this paper 1×10-4 m Length of a typical virus 1×10-8 m Radius of hydrogen atom 5×10-11 m Radius of proton 1×10-15 m 1.3.1 Measurements of Large Distance: P Parallax method θ Large distance, such as the distance of O a planet or a star from the Earth, cannot be measured directly with a metre scale, so a parallax method is used for it. Let us do a simple experiment to understand what is parallax. Hold your hand in front of you and look at E1 O E2 it with your left eye closed and then with your Fig.1.2: Parallax method for determining right eye closed. You will find that your hand distance. appears to move against the background. This effect is called parallax. Parallax is defined as As the distances of planets from the Earth the apparent change in position of an object due are very large, we can not use two eyes method to a change in the position of the observer. By as discussed here. In order to make simultaneous measuring the parallax angle (θ) and knowing observations of an astronomical object, we the distance between the eyes E1E2 as shown in select two distant points on the Earth. Fig. 1.2, we can determine the distance of the Consider two positions A and B on the object from us, i.e., OP as E1E2/θ. surface of Earth, separated by a straight line at 3 distance b as shown in Fig. 1.3. Two observers Planet at these two points observe a distant planet S d simultaneously. We measure the angle ∠ASB between the two directions along which the planet is viewed at these two points. This angle, D represented by symbol θ, is the parallax angle. As the planet is far away, i.e., the distance α of the planet from the Earth is very large in comparison to b, b/D

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