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Measurement of time Accuracy, precision of instruments and errors in measurement Significant figures Dimensions of physical quantities Dimensional formulae and dimensional equations Dimensional analysis and its applications CHAPTER 16 16 18 21 22 22 27 31 31 32 3 MOTION IN A STRAIGHT LINE 3. 1 3. 2 3. 3 3. 4 3. 5 3. 6 3. 7 Introduction Position, path length and displacement Average velocity and average speed Instantaneous velocity and speed Acceleration Kinematic equations for uniformly accelerated motion Relative velocity CHAPTER 39 39 42 43 45 47 51 4 MOTION IN A PLANE 4. 1 4. 2 4. 3 4. 4 4. 5 Introduction
Scalars and vectors Multiplication of vectors by real numbers Addition and subtraction of vectors – graphical method Resolution of vectors 65 65 67 67 69 CK xii 4. 6 4. 7 4. 8 4. 9 4. 10 4. 11 Vector addition – analytical method Motion in a plane Motion in a plane with constant acceleration Relative velocity in two dimensions Projectile motion Uniform circular motion CHAPTER 71 72 75 76 77 79 5 LAWS OF MOTION 5. 1 5. 2 5. 3 5. 4 5. 5 5. 6 5. 7 5. 8 5. 9 5. 10 5. 11 Introduction Aristotle’s fallacy The law of inertia Newton’s first law of motion Newton’s second law of motion Newton’s third law of motion Conservation of momentum
Equilibrium of a particle Common forces in mechanics Circular motion Solving problems in mechanics CHAPTER 89 90 90 91 93 96 98 99 100 104 105 6 WORK, ENERGY AND POWER 6. 1 6. 2 6. 3 6. 4 6. 5 6. 6 6. 7 6. 8 6. 9 6. 10 6. 11 6. 12 Introduction Notions of work and kinetic energy : The work-energy theorem Work Kinetic energy Work done by a variable force The work-energy theorem for a variable force The concept of potential energy The conservation of mechanical energy The potential energy of a spring Various forms of energy : the law of conservation of energy Power Collisions CHAPTER 114 116 116 117 118 119 120 121 123 126 28 129 7 SYSTEM OF PARTICLES AND ROTATIONAL MOTION 7. 1 7. 2 7. 3 7. 4 7. 5 7. 6 7. 7 7. 8 7. 9 7. 10 Introduction Centre of mass Motion of centre of mass Linear momentum of a system of particles Vector product of two vectors Angular velocity and its relation with linear velocity Torque and angular momentum Equilibrium of a rigid body Moment of inertia Theorems of perpendicular and parallel axes 141 144 148 149 150 152 154 158 163 164 CK xiii 7. 11 7. 12 7. 13 7. 14 Kinematics of rotational motion about a fixed axis Dynamics of rotational motion about a fixed axis Angular momentum in case of rotations about a fixed axis
Rolling motion CHAPTER 167 169 171 173 8 GRAVITATION 8. 1 8. 2 8. 3 8. 4 8. 5 8. 6 8. 7 8. 8 8. 9 8. 10 8. 11 8. 12 Introduction Kepler’s laws Universal law of gravitation The gravitational constant Acceleration due to gravity of the earth Acceleration due to gravity below and above the surface of earth Gravitational potential energy Escape speed Earth satellite Energy of an orbiting satellite Geostationary and polar satellites Weightlessness 183 184 185 189 189 190 191 193 194 195 196 197 APPENDICES 203 ANSWERS 219 CK CK CONTENTS FOREWORD PREFACE A NOTE FOR THE TEACHERS CHAPTER iii vii x 9 MECHANICAL PROPERTIES OF SOLIDS 9. 9. 2 9. 3 9. 4 9. 5 9. 6 9. 7 Introduction Elastic behaviour of solids Stress and strain Hooke’s law Stress-strain curve Elastic moduli Applications of elastic behaviour of materials CHAPTER 231 232 232 234 234 235 240 10 MECHANICAL PROPERTIES OF FLUIDS 10. 1 10. 2 10. 3 10. 4 10. 5 10. 6 10. 7 Introduction Pressure Streamline flow Bernoulli’s principle Viscosity Reynolds number Surface tension CHAPTER 246 246 253 254 258 260 261 11 THERMAL PROPERTIES OF MATTER 11. 1 11. 2 11. 3 11. 4 11. 5 11. 6 11. 7 11. 8 11. 9 11. 10 Introduction Temperature and heat Measurement of temperature Ideal-gas equation and absolute temperature
Thermal expansion Specific heat capacity Calorimetry Change of state Heat transfer Newton’s law of cooling CHAPTER 274 274 275 275 276 280 281 282 286 290 12 THERMODYNAMICS 12. 1 12. 2 Introduction Thermal equilibrium 298 299 CK CK xii 12. 3 12. 4 12. 5 12. 6 12. 7 12. 8 12. 9 12. 10 12. 11 12. 12 12. 13 Zeroth law of thermodynamics Heat, internal energy and work First law of thermodynamics Specific heat capacity Thermodynamic state variables and equation of state Thermodynamic processes Heat engines Refrigerators and heat pumps Second law of thermodynamics Reversible and irreversible processes Carnot engine CHAPTER 300 300 302 03 304 305 308 308 309 310 311 13 KINETIC THEORY 13. 1 13. 2 13. 3 13. 4 13. 5 13. 6 13. 7 Introduction Molecular nature of matter Behaviour of gases Kinetic theory of an ideal gas Law of equipartition of energy Specific heat capacity Mean free path CHAPTER 318 318 320 323 327 328 330 14 OSCILLATIONS 14. 1 14. 2 14. 3 14. 4 14. 5 14. 6 14. 7 14. 8 14. 9 14. 10 Introduction Periodic and oscilatory motions Simple harmonic motion Simple harmonic motion and uniform circular motion Velocity and acceleration in simple harmonic motion Force law for simple harmonic motion Energy in simple harmonic motion Some systems executing SHM
Damped simple harmonic motion Forced oscillations and resonance CHAPTER 336 337 339 341 343 345 346 347 351 353 15 WAVES 15. 1 15. 2 15. 3 15. 4 15. 5 15. 6 Introduction Transverse and longitudinal waves Displacement relation in a progressive wave The speed of a travelling wave The principle of superposition of waves Reflection of waves 363 365 367 369 373 374 CK CK xiii 15. 7 15. 8 Beats Doppler effect 379 381 ANSWERS 391 BIBLIOGRAPHY 401 INDEX 403 CK CHAPTER ONE PHYSICAL WORLD 1. 1 WHAT IS PHYSICS ? 1. 1 What is physics ? 1. 2 Scope and excitement of physics 1. 3 Physics, technology and society 1. 4 Fundamental forces in nature 1. Nature of physical laws Summary Exercises Humans have always been curious about the world around them. The night sky with its bright celestial objects has fascinated humans since time immemorial. The regular repetitions of the day and night, the annual cycle of seasons, the eclipses, the tides, the volcanoes, the rainbow have always been a source of wonder. The world has an astonishing variety of materials and a bewildering diversity of life and behaviour. The inquiring and imaginative human mind has responded to the wonder and awe of nature in different ways. One kind of response from the earliest times has been to observe the hysical environment carefully, look for any meaningful patterns and relations in natural phenomena, and build and use new tools to interact with nature. This human endeavour led, in course of time, to modern science and technology. The word Science originates from the Latin verb Scientia meaning ‘to know’. The Sanskrit word Vijnan and the Arabic word Ilm c onvey similar meaning, namely ‘knowledge’. Science, in a broad sense, is as old as human species. The early civilisations of Egypt, India, China, Greece, Mesopotamia and many others made vital contributions to its progress. From the sixteenth century onwards, great strides were made n science in Europe. By the middle of the twentieth century, science had become a truly international enterprise, with many cultures and countries contributing to its rapid growth. What is Science and what is the so-called Scientific Method ? Science is a systematic attempt to understand natural phenomena in as much detail and depth as possible, and use the knowledge so gained to predict, modify and control phenomena. Science is exploring, experimenting and predicting from what we see around us. The curiosity to learn about the world, unravelling the secrets of nature is the first step towards the discovery of science.
The scientific method involves several interconnected steps : Systematic observations, controlled experiments, qualitative and 2 quantitative reasoning, mathematical modelling, prediction and verification or falsification of theories. Speculation and conjecture also have a place in science; but ultimately, a scientific theory, to be acceptable, must be verified by relevant observations or experiments. There is much philosophical debate about the nature and method of science that we need not discuss here. The interplay of theory and observation (or experiment) is basic to the progress of science. Science is ever dynamic.
There is no ‘final’ theory in science and no unquestioned authority among scientists. As observations improve in detail and precision or experiments yield new results, theories must account for them, if necessary, by introducing modifications. Sometimes the modifications may not be drastic and may lie within the framework of existing theory. For example, when Johannes Kepler (1571-1630) examined the extensive data on planetary motion collected by Tycho Brahe (1546-1601), the planetary circular orbits in heliocentric theory (sun at the centre of the solar system) imagined by Nicolas Copernicus (1473–1543) had to be replaced by elliptical rbits to fit the data better. Occasionally, however, the existing theory is simply unable to explain new observations. This causes a major upheaval in science. In the beginning of the twentieth century, it was realised that Newtonian mechanics, till then a very successful theory, could not explain some of the most basic features of atomic phenomena. Similarly, the then accepted wave picture of light failed to explain the photoelectric effect properly. This led to the development of a radically new theory (Quantum Mechanics) to deal with atomic and molecular phenomena. Just as a new experiment may suggest an lternative theoretical model, a theoretical advance may suggest what to look for in some experiments. The result of experiment of scattering of alpha particles by gold foil, in 1911 by Ernest Rutherford (1871–1937) established the nuclear model of the atom, which then became the basis of the quantum theory of hydrogen atom given in 1913 by Niels Bohr (1885–1962). On the other hand, the concept of antiparticle was first introduced theoretically by Paul Dirac (1902–1984) in 1930 and confirmed two years later by the experimental discovery of positron (antielectron) by Carl Anderson. P HYSICS Physics is a basic discipline in the category f Natural Sciences, which also includes other disciplines like Chemistry and Biology. The word Physics comes from a Greek word meaning nature. Its Sanskrit equivalent is Bhautiki that is used to refer to the study of the physical world. A precise definition of this discipline is neither possible nor necessary. We can broadly describe physics as a study of the basic laws of nature and their manifestation in different natural phenomena. The scope of physics is described briefly in the next section. Here we remark on two principal thrusts in physics : unification and reduction. In Physics, we attempt to explain diverse hysical phenomena in terms of a few concepts and laws. The effort is to see the physical world as manifestation of some universal laws in different domains and conditions. For example, the same law of gravitation (given by Newton) describes the fall of an apple to the ground, the motion of the moon around the earth and the motion of planets around the sun. Similarly, the basic laws of electromagnetism (Maxwell’s equations) govern all electric and magnetic phenomena. The attempts to unify fundamental forces of nature (section 1. 4) reflect this same quest for unification. A related effort is to derive the properties of a igger, more complex, system from the properties and interactions of its constituent simpler parts. This approach is called reductionism and is at the heart of physics. For example, the subject of thermodynamics, developed in the nineteenth century, deals with bulk systems in terms of macroscopic quantities such as temperature, internal energy, entropy, etc. Subsequently, the subjects of kinetic theory and statistical mechanics interpreted these quantities in terms of the properties of the molecular constituents of the bulk system. In particular, the temperature was seen to be related to the average kinetic energy of molecules of the system. . 2 SCOPE AND EXCITEMENT OF PHYSICS We can get some idea of the scope of physics by looking at its various sub-disciplines. Basically, there are two domains of interest : macroscopic and microscopic. The macroscopic domain includes phenomena at the laboratory, terrestrial and astronomical scales. The microscopic domain includes atomic, molecular and nuclear P HYSICAL WORLD phenomena*. Classical Physics deals mainly with macroscopic phenomena and includes subjects like Mechanics, Electrodynamics, Optics a nd T hermodynamics . Mechanics founded on Newton’s laws of motion and the law of gravitation is concerned with the motion (or quilibrium) of particles, rigid and deformable bodies, and general systems of particles. The propulsion of a rocket by a jet of ejecting gases, propagation of water waves or sound waves in air, the equilibrium of a bent rod under a load, etc. , are problems of mechanics. Electrodynamics deals with electric and magnetic phenomena associated with charged and magnetic bodies. Its basic laws were given by Coulomb, Oersted, Fig. 1. 1 chemical process, etc. , are problems of interest in thermodynamics. The microscopic domain of physics deals with the constitution and structure of matter at the minute scales of atoms and nuclei (and even ower scales of length) and their interaction with different probes such as electrons, photons and other elementary particles. Classical physics is inadequate to handle this domain and Quantum Theory is currently accepted as the proper framework for explaining microscopic phenomena. Overall, the edifice of physics is beautiful and imposing and you will appreciate it more as you pursue the subject. Theory and experiment go hand in hand in physics and help each other’s progress. The alpha scattering experiments of Rutherford gave the nuclear model of the atom. Ampere and Faraday, and encapsulated by Maxwell in his famous set of equations.
The motion of a current-carrying conductor in a magnetic field, the response of a circuit to an ac voltage (signal), the working of an antenna, the propagation of radio waves in the ionosphere, etc. , are problems of electrodynamics. Optics deals with the phenomena involving light. The working of telescopes and microscopes, colours exhibited by thin films, etc. , are topics in optics. Thermodynamics, in contrast to mechanics, does not deal with the motion of bodies as a whole. Rather, it deals with systems in macroscopic equilibrium and is concerned with changes in internal energy, temperature, entropy, etc. , of the ystem through external work and transfer of heat. The efficiency of heat engines and refrigerators, the direction of a physical or * 3 You can now see that the scope of physics is truly vast. It covers a tremendous range of magnitude of physical quantities like length, mass, time, energy, etc. At one end, it studies phenomena at the very small scale of length -14 (10 m or even less) involving electrons, protons, etc. ; at the other end, it deals with astronomical phenomena at the scale of galaxies or even the entire universe whose extent is of the order of 26 10 m. The two length scales differ by a factor of 40 10 or even more.
The range of time scales can be obtained by dividing the length scales by the –22 speed of light : 10 s to 1018 s. The range of masses goes from, say, 10–30 kg (mass of an 55 electron) to 10 kg (mass of known observable universe). Terrestrial phenomena lie somewhere in the middle of this range. Recently, the domain intermediate between the macroscopic and the microscopic (the so-called mesoscopic physics), dealing with a few tens or hundreds of atoms, has emerged as an exciting field of research. 4 Physics is exciting in many ways. To some people the excitement comes from the elegance and universality of its basic theories, from the fact that few basic concepts and laws can explain phenomena covering a large range of magnitude of physical quantities. To some others, the challenge in carrying out imaginative new experiments to unlock the secrets of nature, to verify or refute theories, is thrilling. Applied physics is equally demanding. Application and exploitation of physical laws to make useful devices is the most interesting and exciting part and requires great ingenuity and persistence of effort. What lies behind the phenomenal progress of physics in the last few centuries? Great progress usually accompanies changes in our basic perceptions.
First, it was realised that for scientific progress, only qualitative thinking, though no doubt important, is not enough. Quantitative measurement is central to the growth of science, especially physics, because the laws of nature happen to be expressible in precise mathematical equations. The second most important insight was that the basic laws of physics are universal — the same laws apply in widely different contexts. Lastly, the strategy of approximation turned out to be very successful. Most observed phenomena in daily life are rather complicated manifestations of the basic laws. Scientists recognised the importance f extracting the essential features of a phenomenon from its less significant aspects. It is not practical to take into account all the complexities of a phenomenon in one go. A good strategy is to focus first on the essential features, discover the basic principles and then introduce corrections to build a more refined theory of the phenomenon. For example, a stone and a feather dropped from the same height do not reach the ground at the same time. The reason is that the essential aspect of the phenomenon, namely free fall under gravity, is complicated by the presence of air resistance. To get the law of free all under gravity, it is better to create a situation wherein the air resistance is negligible. We can, for example, let the stone and the feather fall through a long evacuated tube. In that case, the two objects will fall almost at the same rate, giving the basic law that acceleration due to gravity is independent of the mass of the object. With the basic law thus found, we can go back to the feather, introduce corrections due to air resistance, modify the existing theory and try to build a more realistic P HYSICS Hypothesis, axioms and models One should not think that everything can be proved with physics and mathematics.
All physics, and also mathematics, is based on assumptions, each of which is variously called a hypothesis or axiom or postulate, etc. For example, the universal law of gravitation proposed by Newton is an assumption or hypothesis, which he proposed out of his ingenuity. Before him, there were several observations, experiments and data, on the motion of planets around the sun, motion of the moon around the earth, pendulums, bodies falling towards the earth etc. Each of these required a separate explanation, which was more or less qualitative. What the universal law of gravitation says is that, if we assume that any two odies in the universe attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them, then we can explain all these observations in one stroke. It not only explains these phenomena, it also allows us to predict the results of future experiments. A hypothesis is a supposition without assuming that it is true. It would not be fair to ask anybody to prove the universal law of gravitation, because it cannot be proved. It can be verified and substantiated by experiments and observations. An axiom is a self-evident truth while a model s a theory proposed to explain observed phenomena. But you need not worry at this stage about the nuances in using these words. For example, next year you will learn about Bohr’s model of hydrogen atom, in which Bohr assumed that an electron in the hydrogen atom follows certain rules (postutates). Why did he do that? There was a large amount of spectroscopic data before him which no other theory could explain. So Bohr said that if we assume that an atom behaves in such a manner, we can explain all these things at once. Einstein’s special theory of relativity is also based on two postulates, the constancy of the speed f electromagnetic radiation and the validity of physical laws in all inertial frame of reference. It would not be wise to ask somebody to prove that the speed of light in vacuum is constant, independent of the source or observer. In mathematics too, we need axioms and hypotheses at every stage. Euclid’s statement that parallel lines never meet, is a hypothesis. This means that if we assume this statement, we can explain several properties of straight lines and two or three dimensional figures made out of them. But if you don’t assume it, you are free to use a different axiom and get a new geometry, as has indeed happened in he past few centuries and decades. P HYSICAL WORLD 5 theory of objects falling to the earth under gravity. 1. 3 PHYSICS, TECHNOLOGY AND SOCIETY The connection between physics, technology and society can be seen in many examples. The discipline of thermodynamics arose from the need to understand and improve the working of heat engines. The steam engine, as we know, is inseparable from the Industrial Revolution in England in the eighteenth century, which had great impact on the course of human civilisation. Sometimes technology gives rise to new physics; at other times physics generates new technology.
An example of the latter is the wireless communication technology that followed the discovery of the basic laws of electricity and magnetism in the nineteenth century. The applications of physics are not always easy to foresee. As late as 1933, the great physicist Ernest Rutherford had dismissed the possibility of tapping energy from atoms. But only a few years later, in 1938, Hahn and Meitner discovered the phenomenon of neutron-induced fission of uranium, which would serve as the basis of nuclear power reactors and nuclear weapons. Yet another important example of physics giving rise to technology is the silicon chip’ that triggered the computer revolution in the last three decades of the twentieth century. A most significant area to which physics has and will contribute is the development of alternative energy resources. The fossil fuels of the planet are dwindling fast and there is an urgent need to discover new and affordable sources of energy. Considerable progress has already been made in this direction (for example, in conversion of solar energy, geothermal energy, etc. , into electricity), but much more is still to be accomplished. Table1. 1 lists some of the great physicists, their major contribution and the country of rigin. You will appreciate from this table the multi-cultural, international character of the scientific endeavour. Table 1. 2 lists some important technologies and the principles of physics they are based on. Obviously, these tables are not exhaustive. We urge you to try to add many names and items to these tables with the help of your teachers, good books and websites on science. You will find that this exercise is very educative and also great fun. And, assuredly, it will never end. The progress of science is unstoppable! Physics is the study of nature and natural phenomena. Physicists try to discover the rules hat are operating in nature, on the basis of observations, experimentation and analysis. Physics deals with certain basic rules/laws governing the natural world. What is the nature Table 1. 1 Some physicists from different countries of the world and their major contributions Name Major contribution/discovery Country of Origin Archimedes Principle of buoyancy; Principle of the lever Greece Galileo Galilei Law of inertia Italy Christiaan Huygens Wave theory of light Holland Isaac Newton Universal law of gravitation; Laws of motion; Reflecting telescope U. K. Michael Faraday Laws of electromagnetic induction U. K. James Clerk Maxwell
Electromagnetic theory; Light-an electromagnetic wave U. K. Heinrich Rudolf Hertz Generation of electromagnetic waves Germany J. C. Bose Ultra short radio waves India W. K. Roentgen X-rays Germany J. J. Thomson Electron U. K. Marie Sklodowska Curie Discovery of radium and polonium; Studies on Poland natural radioactivity Albert Einstein Explanation of photoelectric effect; Theory of relativity Germany 6 P HYSICS Name Major contribution/discovery Country of Origin Victor Francis Hess Cosmic radiation Austria R. A. Millikan Measurement of electronic charge U. S. A. Ernest Rutherford Nuclear model of atom New Zealand Niels Bohr
Quantum model of hydrogen atom Denmark C. V. Raman Inelastic scattering of light by molecules India Louis Victor de Borglie Wave nature of matter France M. N. Saha Thermal ionisation India S. N. Bose Quantum statistics India Wolfgang Pauli Exclusion principle Austria Enrico Fermi Controlled nuclear fission Italy Werner Heisenberg Quantum mechanics; Uncertainty principle Germany Paul Dirac Relativistic theory of electron; Quantum statistics U. K. Edwin Hubble Expanding universe U. S. A. Ernest Orlando Lawrence Cyclotron U. S. A. James Chadwick Neutron U. K. Hideki Yukawa Theory of nuclear forces Japan Homi Jehangir Bhabha
Cascade process of cosmic radiation India Lev Davidovich Landau Theory of condensed matter; Liquid helium Russia S. Chandrasekhar Chandrasekhar limit, structure and evolution of stars India John Bardeen Transistors; Theory of super conductivity U. S. A. C. H. Townes Maser; Laser U. S. A. Abdus Salam Unification of weak and electromagnetic interactions Pakistan of physical laws? We shall now discuss the nature of fundamental forces and the laws that govern the diverse phenomena of the physical world. 1. 4 FUNDAMENTAL FORCES IN NATURE* We all have an intuitive notion of force. In our experience, force is needed to push, carry or hrow objects, deform or break them. We also experience the impact of forces on us, like when a moving object hits us or we are in a merry-goround. Going from this intuitive notion to the proper scientific concept of force is not a trivial matter. Early thinkers like Aristotle had wrong * ideas about it. The correct notion of force was arrived at by Isaac Newton in his famous laws of motion. He also gave an explicit form for the force for gravitational attraction between two bodies. We shall learn these matters in subsequent chapters. In the macroscopic world, besides the gravitational force, we encounter several kinds f forces: muscular force, contact forces between bodies, friction (which is also a contact force parallel to the surfaces in contact), the forces exerted by compressed or elongated springs and taut strings and ropes (tension), the force of buoyancy and viscous force when solids are in Sections 1. 4 and 1. 5 contain several ideas that you may not grasp fully in your first reading. However, we advise you to read them carefully to develop a feel for some basic aspects of physics. These are some of the areas which continue to occupy the physicists today. P HYSICAL WORLD 7 Table 1. 2 Link between technology and physics Technology
Scientific principle(s) Steam engine Laws of thermodynamics Nuclear reactor Controlled nuclear fission Radio and Television Generation, propagation and detection of electromagnetic waves Computers Digital logic Lasers Light amplification by stimulated emission of radiation Production of ultra high magnetic fields Superconductivity Rocket propulsion Newton’s laws of motion Electric generator Faraday’s laws of electromagnetic induction Hydroelectric power Conversion of gravitational potential energy into electrical energy Aeroplane Bernoulli’s principle in fluid dynamics Particle accelerators Motion of charged particles in electromagnetic ields Sonar Reflection of ultrasonic waves Optical fibres Total internal reflection of light Non-reflecting coatings Thin film optical interference Electron microscope Wave nature of electrons Photocell Photoelectric effect Fusion test reactor (Tokamak) Magnetic confinement of plasma Giant Metrewave Radio Telescope (GMRT) Detection of cosmic radio waves Bose-Einstein condensate Trapping and cooling of atoms by laser beams and magnetic fields. contact with fluids, the force due to pressure of a fluid, the force due to surface tension of a liquid, and so on. There are also forces involving charged nd magnetic bodies. In the microscopic domain again, we have electric and magnetic forces, nuclear forces involving protons and neutrons, interatomic and intermolecular forces, etc. We shall get familiar with some of these forces in later parts of this course. A great insight of the twentieth century physics is that these different forces occurring in different contexts actually arise from only a small number of fundamental forces in nature. For example, the elastic spring force arises due to the net attraction/repulsion between the neighbouring atoms of the spring when the spring is elongated/compressed. This net ttraction/repulsion can be traced to the (unbalanced) sum of electric forces between the charged constituents of the atoms. In principle, this means that the laws for ‘derived’ forces (such as spring force, friction) are not independent of the laws of fundamental forces in nature. The origin of these derived forces is, however, very complex. At the present stage of our understanding, we know of four fundamental forces in nature, which are described in brief here : 8 P HYSICS Albert Einstein (1879-1955) Albert Einstein, born in Ulm, Germany in 1879, is universally regarded as one of the greatest physicists of all time.
His astonishing scientific career began with the publication of three path-breaking papers in 1905. In the first paper, he introduced the notion of light quanta (now called photons) and used it to explain the features of photoelectric effect that the classical wave theory of radiation could not account for. In the second paper, he developed a theory of Brownian motion that was confirmed experimentally a few years later and provided a convincing evidence of the atomic picture of matter. The third paper gave birth to the special theory of relativity that made Einstein a legend in his own life time.
In the next decade, he explored the consequences of his new theory which included, among other things, the mass-energy equivalence enshrined in his famous equation E = mc2. He also created the general version of relativity (The General Theory of Relativity), which is the modern theory of gravitation. Some of Einstein’s most significant later contributions are: the notion of stimulated emission introduced in an alternative derivation of Planck’s blackbody radiation law, static model of the universe which started modern cosmology, quantum statistics of a gas of massive bosons, and a critical analysis of the foundations of quantum mechanics.
The year 2005 was declared as International Year of Physics, in recognition of Einstein’s monumental contribution to physics, in year 1905, describing revolutionary scientific ideas that have since influenced all of modern physics. 1. 4. 1 Gravitational Force The gravitational force is the force of mutual attraction between any two objects by virtue of their masses. It is a universal force. Every object experiences this force due to every other object in the universe. All objects on the earth, for example, experience the force of gravity due to the earth. In particular, gravity governs the motion of the moon and artificial satellites around he earth, motion of the earth and planets around the sun, and, of course, the motion of bodies falling to the earth. It plays a key role in the large-scale phenomena of the universe, such as formation and evolution of stars, galaxies and galactic clusters. 1. 4. 2 Electromagnetic Force Electromagnetic force is the force between charged particles. In the simpler case when charges are at rest, the force is given by Coulomb’s law : attractive for unlike charges and repulsive for like charges. Charges in motion produce magnetic effects and a magnetic field gives rise to a force on a moving charge. Electric nd magnetic effects are, in general, inseparable – hence the name electromagnetic force. Like the gravitational force, electromagnetic force acts over large distances and does not need any intervening medium. It is enormously strong compared to gravity. The electric force between two protons, for example, 36 is 10 times the gravitational force between them, for any fixed distance. Matter, as we know, consists of elementary charged constituents like electrons and protons. Since the electromagnetic force is so much stronger than the gravitational force, it dominates all phenomena at atomic and molecular scales. (The other two forces, as we hall see, operate only at nuclear scales. ) Thus it is mainly the electromagnetic force that governs the structure of atoms and molecules, the dynamics of chemical reactions and the mechanical, thermal and other properties of materials. It underlies the macroscopic forces like ‘tension’, ‘friction’, ‘normal force’, ‘spring force’, etc. Gravity is always attractive, while electromagnetic force can be attractive or repulsive. Another way of putting it is that mass comes only in one variety (there is no negative mass), but charge comes in two varieties : positive and negative charge. This is what makes all the difference.
Matter is mostly electrically neutral (net charge is zero). Thus, electric force is largely zero and gravitational force dominates terrestrial phenomena. Electric force manifests itself in atmosphere where the atoms are ionised and that leads to lightning. P HYSICAL WORLD 9 Satyendranath Bose (1894-1974) Satyendranath Bose, born in Calcutta in 1894, is among the great Indian physicists who made a fundamental contribution to the advance of science in the twentieth century. An outstanding student throughout, Bose started his career in 1916 as a lecturer in physics in Calcutta University; five years later he joined Dacca University.
Here in 1924, in a brilliant flash of insight, Bose gave a new derivation of Planck’s law, treating radiation as a gas of photons and employing new statistical methods of counting of photon states. He wrote a short paper on the subject and sent it to Einstein who immediately recognised its great significance, translated it in German and forwarded it for publication. Einstein then applied the same method to a gas of molecules. The key new conceptual ingredient in Bose’s work was that the particles were regarded as indistinguishable, a radical departure from the assumption that underlies the classical MaxwellBoltzmann statistics.
It was soon realised that the new Bose-Einstein statistics was applicable to particles with integers spins, and a new quantum statistics (Fermi-Dirac statistics) was needed for particles with half integers spins satisfying Pauli’s exclusion principle. Particles with integers spins are now known as bosons in honour of Bose. An important consequence of Bose-Einstein statistics is that a gas of molecules below a certain temperature will undergo a phase transition to a state where a large fraction of atoms populate the same lowest energy state.
Some seventy years were to pass before the pioneering ideas of Bose, developed further by Einstein, were dramatically confirmed in the observation of a new state of matter in a dilute gas of ultra cold alkali atoms – the Bose-Eintein condensate. If we reflect a little, the enormous strength of the electromagnetic force compared to gravity is evident in our daily life. When we hold a book in our hand, we are balancing the gravitational force on the book due to the huge mass of the earth by the ‘normal force’ provided by our hand. The latter is nothing but the net electromagnetic force between the charged constituents of our hand and he book, at the surface in contact. If electromagnetic force were not intrinsically so much stronger than gravity, the hand of the strongest man would crumble under the weight of a feather ! Indeed, to be consistent, in that circumstance, we ourselves would crumble under our own weight ! 1. 4. 3 Strong Nuclear Force The strong nuclear force binds protons and neutrons in a nucleus. It is evident that without some attractive force, a nucleus will be unstable due to the electric repulsion between its protons. This attractive force cannot be gravitational since force of gravity is negligible compared to the electric force.
A new basic force must, therefore, be invoked. The strong nuclear force is the strongest of all fundamental forces, about 100 times the electromagnetic force in strength. It is charge-independent and acts equally between a proton and a proton, a neutron and a neutron, and a proton and a neutron. Its range is, however, extremely small, –15 of about nuclear dimensions (10 m). It is responsible for the stability of nuclei. The electron, it must be noted, does not experience this force. Recent developments have, however, indicated that protons and neutrons are built out of still more elementary constituents called quarks. . 4. 4 Weak Nuclear Force The weak nuclear force appears only in certain nuclear processes such as the ? -decay of a nucleus. In ? -decay, the nucleus emits an electron and an uncharged particle called neutrino. The weak nuclear force is not as weak as the gravitational force, but much weaker than the strong nuclear and electromagnetic forces. The range of weak nuclear force is exceedingly small, of the order of 10-16 m. 1. 4. 5 Towards Unification of Forces We remarked in section 1. 1 that unification is a basic quest in physics. Great advances in physics often amount to unification of different 10 P HYSICS Table 1. Fundamental forces of nature Name Relative strength Range Operates among Gravitational force 10 –39 Infinite All objects in the universe Weak nuclear force 10–13 Very short, Sub-nuclear size ( ? –16 m) 10 Some elementary particles, particularly electron and neutrino Electromagnetic force 10–2 Infinite Charged particles Strong nuclear force 1 Short, nuclear size ( ? –15 m) 10 Nucleons, heavier elementary particles theories and domains. Newton unified terrestrial and celestial domains under a common law of gravitation. The experimental discoveries of Oersted and Faraday showed that electric and magnetic phenomena are in general nseparable. Maxwell unified electromagnetism and optics with the discovery that light is an electromagnetic wave. Einstein attempted to unify gravity and electromagnetism but could not succeed in this venture. But this did not deter physicists from zealously pursuing the goal of unification of forces. Recent decades have seen much progress on this front. The electromagnetic and the weak nuclear force have now been unified and are seen as aspects of a single ‘electro-weak’ force. What this unification actually means cannot be explained here. Attempts have been (and are being) made to unify the electro-weak and the trong force and even to unify the gravitational force with the rest of the fundamental forces. Many of these ideas are still speculative and inconclusive. Table 1. 4 summarises some of the milestones in the progress towards unification of forces in nature. 1. 5 NATURE OF PHYSICAL LAWS Physicists explore the universe. Their investigations, based on scientific processes, range from particles that are smaller than atoms in size to stars that are very far away. In addition to finding the facts by observation and experimentation, physicists attempt to discover the laws that summarise (often as mathematical quations) these facts. In any physical phenomenon governed by different forces, several quantities may change with time. A remarkable fact is that some special physical quantities, however, remain constant in time. They are the conserved quantities of nature. Understanding these conservation principles is very important to describe the observed phenomena quantitatively. For motion under an external conservative force, the total mechanical energy i. e. the sum of kinetic and potential energy of a body is a constant. The familiar example is the free fall of an object under gravity. Both the kinetic energy