G R Bathla & Sons is a leading publishing house in India located at Meerut. GRB Publication played a pivotal role in bringing my five GRB Understanding Physics books to life, significantly transformed my career as a physics author-educator. This significance of these books is noteworthy; the first two books’ Mechanics Part -A and Mechanics Part- B for JEE (Main & Advanced) gained unprecedented support from the potential educators and students across the country due to its original innovative problems. The 3rd book Electromagnetism is a stuffy book with deep rooted ideas with new approach. The 4th book Wave, Heat & Thermodynamics is a creamy, short and concise. The 5th book Optics & Modern Physics carries a unique styled for JEE (Main & Advanced). All these books are cornerstones for JEE aspirants, and GRB’s support was instrumental in their success.

 

GRB’s expertise in educational publishing ensured that each book was meticulously crafted to meet the needs of competitive exam students. Their editorial team collaborated closely with me to refine content, ensuring clarity in explanations and alignment with JEE syllabi. For instance, in Electromagnetism, GRB’s input helped streamline complex topics like Maxwell’s equations, making them accessible yet rigorous. Their focus on quality production—clear diagrams, structured layouts, and error-free problem sets—enhanced the books’ appeal, as seen in Mechanics Part B, where detailed solutions to rotational dynamics problems became a student favourite.

 

GRB’s robust distribution network was a game-changer, placing my books in bookstores, coaching centres, and online platforms across India. This wide reach, coupled with their marketing efforts amplified my influence in physics education in India. Their reputation in the JEE preparation market lent credibility, attracting a loyal readership. Additionally, GRB’s commitment to timely publication ensured Wave Heat & Thermodynamics and Optics & Modern Physics met market demand, reinforcing my relevance.

 

By providing a platform to share my expertise, GRB empowered me to shape JEE preparation, fostering a community of physics enthusiasts. Their partnership elevated my books into trusted resources, solidifying my legacy as an educator-author.

 

 

 

This series comprises five books on entire physics; Mechanics Part-A, Mechanics Part-B, Electromagnetism, Wave Heat & Thermodynamics, and Optics & Modern Physics. It is a cornerstone for JEE preparation. These books are lauded for their structured approach, blending clear explanations with challenging problems that mirror exam patterns.

 

 

Mechanics Part-A

It explains the particle mechanics by dividing the system in to three parts such as pulley-string-particle, spring-particle and wedge-particle. Then, it describes how to solve the problems by using the concepts Newton’s laws, work-energy theorem and conservation of energy.

 

Mechanics Part-B

It contains centre of mass, mechanics of rigid bodies, fluid mechanics, properties of matter etc., are many-particle systems. The book tells us how to use the Newton’s laws, work-energy theorem, laws of conservation of energy, linear and angular momentum for these many-particle systems. It elucidates the deeper concepts with innovative examples.

 

 

Electromagnetism

It presents the subtle ideas of field and potential and derives the relation between these two concepts by using work-energy theorem. The lucid explanation of field and potential in a conductor and dielectrics simplifies the understanding of the concept of capacitance. The concepts of resistance, Ohm’s law, Kirchoff’s circuital laws in current electricity are explained by using the mechanical laws of conservation of energy and work-energy theorem. The baffling properties of static and time varying magnetic field and induced electric field are explained with utmost care by interpreting the inductance. At last, the response of resistance, capacitance and inductance to an alternating current are explained with a resonant condition.

 

Waves, Heat and Thermodynamics

This book deals with the subject in a different way as compared to other books. It derives of equations of wave mechanics by using Newton’s laws and Hooke’s law. Then, it explains the energy exchange in the process of wave transmission by applying work-energy theorem. The interference and stationary waves are explained in both transverse and longitudinal waves as two types of superpositions of waves. The concept of beat is explained as the third type of superposition in longitudinal (sound) waves. Doppler’s effect of sound is explained from the basics.

 

   An ideal gas is a system of particles that obeys work-energy theorem and law of energy-conservation. This explains the 1st law of thermodynamics as a manifestation of work-energy theorem to an ideal gas. Then, it tells us how to apply this law to solve the problems of expansion of an ideal gas. The concept of thermal stress in the expansion of solid, coefficient of apparent expansion in liquids and the related problems combining these two are explained carefully.

 

 

Optics & Modern Physics

This book presents optics in two chapters such as geometrical (ray) optics and wave optics. The modern physics is comprised of three chapters such as wave and particle nature of radiation, wave and particle nature of matter and nuclear physics. As the division of the chapters are totally different from other existing books, the approach is totally nontraditional and student-friendly. The chapters are interconnected by proper description of the histories of physics - how the theories were naturally developed following the past and existing theories. This connects the theories (quantum mechanics) to technologies like photovoltaic, photoelectric effect, lasers etc., fostering student curiosity.

 

           IOP Publishing is a prestigious international publishing house in Bristol in United Kingdom. It is a subsidiary of Institute of Physics, London. This elevated my books, Problems and Solutions in Rotational Mechanics and Problems and Solutions in Many-Particle Systems, by providing global reach, rigorous peer review, and a prestigious platform. Their expertise ensured high-quality production, enhancing credibility and visibility among JEE aspirants and educators, significantly boosting my career in physics education. This series is comprised of the following six books:

 

1. Problems and Solutions in Rotational Mechanics

2. Problems and Solutions in Many-particle System

3. Problems and Solutions in Electricity and Magnetism

4. Problems and Solutions in Oscillations and Waves, Heat and Thermodynamics

5. Problems and Solutions in Optics and Modern Physics

 

 

Overview of the series

From my student hood to till date I am in search of a series of books on College Physics that carries every concept in deep along with the scholarly problems to cater the needs of potential students preparing for top entrance examinations. I found the students and scholars spending hundreds of hours to gather the information from different sources, websites, books on each concept and chapter. This practice continues till to date. This is due to the lack of a desired college physics book-series. We have a lot of books in the market; each has its own merits and limitations. Practically, it is not possible to get everything in a single book. However, a potential student expects everything in a book such as varieties of adequate problems with detailed theories and solved examples.

             Students are confused by the scattered and variety of sources for the problems, as well as their provenance and validity of solutions. So, not only do helpless students but also the teachers need concise and precise books containing exercises where maximum concepts are covered systematically. The proposed series of books is a sincere effort to minimise all the above limitations of existing books and resources and maximise the potential of the books in terms of content, quality, rigor, and depth in theories, questions, and problems.

            There are no such books available in the market balanced with problems, theories, quality, and quantity of the problems. In this series, we have attempted to balance the books with theories, examples, and problems using a systematic approach for concept building. By virtue of my experience and expertise and suggestions and recommendations of my colleagues and hundreds of my gifted students, the proposed series of books is an outcome of my aim to transform physics-phobia into a physics-loving attitude for students.

 

Readership

At present, sophomores prepare for entrance examinations to get into premier universities like Oxford, Cambridge, etc., in the United Kingdom; MIT, Princeton, etc, in the Unites States of America. Millions of students all over the world appear for Physics Olympiads (both national and international) and other international physics examinations such as Physics GRE, etc. In India, millions of students appear for national-level examinations for prestigious Indian Institutes of Technology (IITs) through a toughest Joint Entrance Examination called IIT-JEE with a lowest success rate in the world.

Moreover, this book is also useful for students preparing for the PhD qualifying examinations of top universities and Physics GRE examinations. In India, students preparing for UPSC examinations and semester examinations and Physics majors in BSc and BEng (or any branch of engineering study) can use this book as a handbook of physics problems. This book will be ultimately useful for Indian students preparing for JEE (Mains and Advanced).

  To educate potential students, teachers should be strong in concepts and problem-solving ability. I strongly hope that this text could be a valuable reference book for JEE-educators in India due to its content and quality such a familiar problems, theories, creative problems, and problems with detailed solutions along with impressive coloured diagrams throughout. I have handpicked many problems from various sources. Each problem is observed being asked in different ways in various examinations all over the world. I spent adequate time in analysing each problem’s, most original version and then put it in my series. Furthermore, I prefer to put all possible questions linked with the original problems in one place so that the students do not have to waste their time to think too much and wander.

 

How to Use These Books

Students should first complete the given theory with the examples and then try to solve the problems without referring the solution by in their own ways. Sometimes students find better methods for solving the problems and should not rely solely on the methods provided. However, if a student falters after repeated attempts, they can refer to the given solutions. Although I tried to create an error-free text, some unavoidable mistakes might appear in some subtle form each time. So, always there will be a scope of improvement of the content. I request my readers to critically analyse my work and give their valuable comments and suggestions for the overall improvement of this book and make this book error-less in due course of time.

 

 

 

 

 

1. Problems and Solutions in Rotational Mechanics

Rotational mechanics is a rank-deciding area in examinations for aspiring students. Due to its complexity average students have a fear of this area. Thus, I have tried to present the subject matter in an interesting way without the use of higher mathematics such as Langrangian, Hamiltonian, etc. I present the examples and problems in a proper sequence following the theories. Rotational mechanics is the most challenging area in mechanics because it needs many concepts to solve a single problem. The correct solution of a single problem in this area will greatly improve the ranking of a student. Thus, this portion is a rank-deciding one. Thus, each aspiring student seeks an appropriate book of rotational mechanics that could fulfil all the criteria, but to my knowledge there is no such single book. Thus, I hope this book could be of unique value for those students. This book has five chapters: 1. Kinematics of rotation 2. Torque and angular momentum for a point mass 3. The statics and dynamics of rigid bodies 4. The energy of rigid bodies 5. Impulse and momentum of rigid bodies. The first chapter discusses the angular quantities, such as angular displacement, angular velocity, and angular acceleration, the kinematics of rolling, and the instantaneous axis of rotation. The second chapter establishes two key concepts, xiv Problems and Solutions in Rotational Mechanics namely torque and angular momentum, for the motion of a particle. The third chapter extends the application of torque and angular momentum for a system of particles and then for rigid bodies. The fourth chapter deals with the energy aspect of a rigid body, such as translational and rotational kinetic energy. The application of the work–energy theorem and energy conservation are described in this chapter. The last chapter deals with the impulse–momentum equations applied for a rigid body. The principle of conservation of angular momentum is explained with many interesting examples including the collision of rigid bodies.

 

 

2. Problems and Solutions in Particle Mechanics

Particle mechanics deals with the kinematics and dynamics of a point mass or particle. In this book the application of kinematics, Newton’s laws and all conservation laws etc., on a particle. This will form the basics of mechanics of many-particle system (fluid mechanics, thermodynamics etc.). This book contains six chapters: 1. Vectors 2. Motion in one dimension 3. Motion in two and three dimension 4. Newton’s laws 5. Friction 6. Circular motion 7. Work, Energy and Power. The first chapter introduces the concept of vector by using the most practical idea of displacement vector. Vector algebra (Addition, subtraction and multiplication of vectors) and vector calculus (differentiation and integration of vectors) are explained. The 2nd chapter deals with the concept of position, velocity and acceleration and its application for a particle moving in a straight line by including the freely falling bodies. All kinematical equations are derived using the vector mathematics which can be used in the 3rd chapter that includes relative motion, projectile motion and circular motion etc.4th chapter deals with the application of Newton’s laws for a particle connected with a spring, string and an inclined plane pr wedge etc. 5th chapter extends the application of Newton’s laws by introducing friction. The condition and laws of static and kinetic friction are explained carefully by suitable examples.6th chapter extends the application of Newton’s laws and kinematics for a particle moving in a curve or circle. The baffling concepts of centripetal and centrifugal forces are scrupulously dealt. The role of friction in circular motion is explained with practical problems. In the last or 7th chapter, the concept of mechanical work and kinetic energy are derived from Newton’s 2nd law and kinematics. This is known as work-kinetic energy theorem. Then, the concept of potential energy is explained for the conservative systems. The use of work- energy theorem is explained by many familiar examples. For conservative systems, the conservation of mechanical energy is explained. Finally, the relation between force and potential energy F=-dU/dx is derived and explained in three types of equilibrium (stable, unstable and neutral).

 

3. Problems and Solutions in Many-particle system

Mechanics of many-particle system (centre of mass, collision, gravitation, fluid mechanics, properties of matter). This book contains six chapters: 1. System of particles 2. Collision 3. Gravitation 4. Fluid statics 5. Fluid dynamics 6. Properties of matter. The first chapter introduces the concept of centre of mass in order to apply Newton’s laws and work–energy theorem for a system of particles. The end of the f irst chapter deals with the impulse-momentum equations for a system of particles. The second chapter deals with the basics of collision. Generally, we use Newton’s impact or empirical formula (NIF) and conservation of momentum for a system of particles that forms the basis of explaining the other chapters such as gravitation, fluid mechanics (static and dynamics), and properties of matter (elasticity, surface tension, capillary action, and viscosity).

 

4. Problems and Solutions in Electricity and Magnetism

This book contains ten chapters 1. Electric field and potential 2. Properties of conductors and dielectrics 3. Capacitance 4. Current, Resistance and Electromotive Force (EMF) 5. Direct Current Circuits 6. Magnetic field   7. Magnetic force and Energy   8. Electromagnetic Induction   9. Inductance 10. Alternating Current.

 The first chapter introduces the concept of electrostatic force by Coulomb’s law. The electric force defines electric field and the concept of work-energy defines electric potential. Then the calculation of electric field is done by using both Coulomb’s law and Gauss’ law for some known charge configurations. By using the field ideas, the calculation of electric potential is done for different charge configurations. At the end of the electrostatics, the field and potential calculation of an electric dipoles is discussed. Furthermore, I explained the interaction of a dipole with an external electric field.

In the 2nd chapter I define the concepts of conductors, dielectric and insulators and discuss their properties. Using these ideas of conductors and dielectric, the first passive electric circuit element, that is, capacitance (C), is explained in the 3rd chapter. Thus, first three chapters deal with electrostatics.

The 4th and 5th chapters deal with current electricity. In 4th chapter, I define the electric current. The second passive circuit element, that is, resistance (R) and the active circuit element electromotive force (emf) that causes a current, are explained. The relation between voltage (potential difference in rough sense) and current is established in the form of Ohm’s law. In 5th chapter Kirchoff’s voltage and current laws and their applications for different direct current circuits are discussed. At the end of this chapter, RC circuits and its response to DC is also discussed. Furthermore, different measuring instruments such as voltmeter, ammeter, meter bridge, potentiometer etc., are explained.

Magnetism is dealt in 6th and 7th chapters. In 6th chapter, magnetic field is defined and by using Biot-Savart’s law and Ampere circuital law, the calculation of magnetic field is explained. In 7th chapter, the interaction of a magnet or current carrying conductor with an external magnetic field or another current carrying system is discussed by Ampere’s force law, in the form of force, energy etc. At the end of the magnetostatics, the field and potential calculation of a magnetic dipole is discussed. Furthermore, I explained the interaction of a magnetic dipole with an external magnetic field of permanent magnets or electromagnets.

The 8th chapter deals with the generation of electricity governed by Faraday’s law of electromagnetic induction and its application such as electric generators, transformers etc. In the 9th chapter the third passive circuit element, that is, inductance (L)is defined. Calculation of self-inductance and mutual-inductance for different current carrying systems is discussed. The response of RL circuit with DC is also discussed at the end of this chapter. In the 10th chapter, I define the alternating current (AC) that is obtained by an alternating current generator discussed in the 9th chapter. I explained the response of the electric passive circuit elements such as resistance (R), Capacitance (C) and inductance (L) to an AC supply in the form of reactance and impedance. Series and parallel RLC circuits are dealt in AC fundamentals in resonance condition.

 

5. Problems and Solutions in Oscillations and Waves, Heat and Thermodynamics

This book contains five chapters

     1. Simple Harmonic Motion

     2. Transverse Waves (Waves in a String)

     3. Longitudinal (Sound) Waves

     4. Kinetic Theory of Gases and Laws of Thermodynamics (KTG)

     5. Temperature and Heat

 

Oscillations (Simple Harmonic Motion)

An oscillation can be simple harmonic if the particle has equal amplitude in both sides of the mean position. An oscillating particle must experience a restoring force that always opposes the displacement from the mean or stable equilibrium. There are various kinds of oscillations of particles such as spring-mass system, simple pendulum etc. The oscillation of rigid bodies can also be categorised into physical pendulums, rolling bodies connected with springs, torsional oscillations etc. Furthermore, the allied problems of oscillation of liquids in a U- and V-tubes and oscillation of a smooth piston in a gas jar, oscillation of a body connected with springs etc. This chapter forms the basis of wave motion.

 

Transverse Waves (Waves in a String)

Wave is a phenomenon in which transfer of both momentum and kinetic energy take place. Waves can be transverse and longitudinal. In a transverse wave, particles move perpendicular to the wave motion. If you flip one end of a hanging string, transverse wave pulse can be produced; however, flipping the end by vibrator, harmonic waves will be produced. There are two types of waves such as travelling or progressive and stationary or standing. Wave propagation takes place due to the inertia and elasticity of the medium in a wave. A stationary wave is the combination of two identical travelling sinusoidal waves. First of all, you can find the speed of a transverse wave in a stretched string by applying Newton’s 2nd law and Hooke’s law. Then, you will be able to determine the power, energy and intensity of a transverse wave. At the end of the chapter the resonant standing waves in a sonometer wire (stretched string) are explained. Thus, in this chapter you will learn the generation, transmission, reflection, superposition (interference and stationary wave) etc., of a transverse wave.

 

Longitudinal Waves

In a longitudinal wave, particles move along the line of wave propagation. Sound waves are longitudinal mechanical waves and they travel through any material medium with a speed that depends on the properties of the medium. As sound wave travels through air, the elements of air vibrate to produce changes in density and pressure along the direction of motion of the wave. If the source of the sound waves vibrates sinusoidally, the pressure variation is also sinusoidal which is known as sinusoidal or harmonic pressure waves. In this chapter the generation, transmission, reflection, superposition (interference, stationary wave and beats) etc., of longitudinal waves are described. The resonant longitudinal standing waves in organ pipes are explained. Furthermore, you will distinguish the pitch, intensity and loudness of sound. A special type of superposition of harmonic longitudinal wave, that is, beat is described. The production of beating effect of sound is explained as doppler’s effect when there is a relative motion between the source and observer or receiver.

 

Kinetic Theory of Gases and Laws of Thermodynamics (KTG)

The 1st  part of this chapter deals with the kinetic theory of gases which is a scientific concept that describes the thermal properties such as  pressure, temperature etc., in terms of the speeds of the gas particles (atoms and molecules).Maxwell-Boltzmann speed distribution of gas molecules forms the basis of this chapter that describes the proportion of molecules having a certain velocity in a specific range.  This continuous collision of the gas particles results a thrust (force) on the container. This force per unit area of the wall gives you the pressure of the gas.

The 2nd part of this chapter deals with thermodynamics that explains the various process or change of state (pressure, volume and temperature) of gases; i.e. as isothermal, adiabatic etc. using the first law of thermodynamics. The application of 2nd law of thermodynamics is also presented with real life examples of refrigerator etc.

 

Temperature and Heat

Heat is the total energy of the motion of the molecules of a substance, whereas temperature refers to the measure of the average energy of the motions of the molecules in the substance. Temperature defines the degree of “hotness” or “coolness” of our surrounding objects. The temperature is measured with a thermometer. The increase in temperature not only increases the internal energy of matter but also causes an expansion of solid, liquid and gases which is described in a separate section. The concept of thermal stress is discussed. Furthermore, the difference between the relative change in length due to temperature rise and the strain caused by the application of a force is clearly explained.

  The last half of this chapter explains with the concept of calorimetry (exchange of heat) by defining the concepts of specific heat, latent heat, heat capacity. Finally, it deals with the transmission (conduction, convection and radiation) of heat by explaining various laws such as Plank’s law, Stefan’s law of radiation, Newton’s laws of cooling etc.

 

6. Problems and Solutions in Optics and Modern Physics

This book has two sections; one is Optics and the other is modern physics. The optics has two chapters such as geometrical or ray optics and wave optics. Geometrical optics deals with reflection and refraction of light in plane and curved surfaces such as mirror, glass slab, prism and lenses. Then we have the wave optics that deals with interference of light in Young’s double slit experiment (YDSE) and its modified form. The 2nd part of the book, that is, modern physics is comprised of three chapters such as wave and particle nature of radiation, wave and particle nature of matter and nuclear physics. The 1st chapter of modern physics describes black body radiation, photoelectric effect, X-rays etc., with proper historical evidence. The 2nd chapter of modern physics deals with atomic structure and matter waves. The 3rd chapter (nuclear physics) tells us about the nucleus with all fundamental laws such as law of radioactivity, mass energy equivalence, alpha, beta, gamma decay etc. At last, the artificial radioactivity is discussed with nuclear fusion and fission.

 

Intension of writing the IOP books

My intension behind this series is two; The first intension is to present some of the original content of much demanded and out of print “GRB Understanding Physics” book in a modified manner for the global audience. My 2nd intension is to present best problems for in-depth theoretical understanding maintaining a proper sequence with coloured diagrams and innovative problems.

Motto of writing the IOP books

My motto is  –  Physics Knowledge Enhancement