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NEWTON LAWS OF MOTION

Introduction to Mechanics

1 Topic

Introduction to Mechanics

Normal Reaction

2 Topics

Normal Reaction

Problems on Normal Reaction

2 Topics | 1 Quiz

Problems on Tension

PROPAGATION OF EM WAVE AND GAUGE TRANSFORMATION MCQ LEVEL-2

2 Topics

Pseudo Forces-contd

Quizzes on Newton Laws of Motion

5 Quizzes

NEWTON'S LAW OF MOTION - MCQ -LEVEL -1

NEWTON’S LAW OF MOTION – MCQ – LEVEL – 2

NEWTON'S LAW OF MOTION – MSQ

NEWTON'S LAW OF MOTION - NAT- LEVEL - 1

NEWTON'S LAW OF MOTION - NAT- LEVEL-2

FRICTION

2 Topics

Problems on Friction

Quizzes on Friction

5 Quizzes

FRICTION FORCE – MCQ – LEVEL – 1

FRICTION FORCE - MCQ - LEVEL - 2

FRICTION FORCE – MSQ

FRICTION FORCE – NAT – LEVEL – 1

FRICTION FORCE – NAT - LEVEL – 2

VELOCITY AND ACCELERATION

Velocity and Acceleration

2 Topics

Velocity and Acceleration

Problems on Velocity and Acceleration

CENTRAL FORCES

Equivalent One Body Problem

3 Topics

Definition of Central Forces

Equivalent One Body Problem

Motion of Double Stars

Conservation laws in Central Force Motion

2 Topics

Conservation of Energy

Conservation of Angular Momentum

Trajectory of Particle Undergoing Central Force Motion

3 Topics

Trajectory of the Particle Undergoing Central Force Motion

Equation of Orbit

Problems on Equation of Orbit

Types of Central Force Motion

4 Topics

Boundedness and Unboundedness

Condition of the Central Force Motion

Central Force Motion under Inverse Square Law Forces

Problems on Central Forces

4 Topics

Problems on Central Forces-1

Problems on Central Forces-2

Problems on Central Forces-3

Problems on Central Forces-4

2 Topics

Problems on Gravitational Forces

Gravitational Field

4 Topics

Gravitational Field

Gravitational Field due to Ring and Disc

Gauss Law of Gravitation

Problems on Gauss Law of Gravitation

Gravitational Potential

3 Topics

Gravitational Potential

Gravitational Potential due to Ring

Gravitational Potential due to Spherical Shell and Solid Sphere

Gravitational Potential Energy

5 Topics

Gravitational Potential Energy

Gravitational Potential Energy for System of Discrete Particles

Gravitational Potential Energy under Gravity

Differential Form of Gauss Law of Gravitation

Gravitational Potential Energy for System of Continuous Mass Distribution

Previous Year Problems on Central Forces in IISc

1 Topic

Previous Year Problems on Central Forces in IISc

Previous Year Problems on Central Forces in JEST

1 Topic

Previous Year Problems on Central Forces in JEST

Previous Year Problems on Central Forces in TIFR

1 Topic

Previous Year Problems on Central Forces in TIFR

Quizzes on Central Forces

5 Quizzes

CENTRAL FORCES – MCQ - LEVEL – 1

CENTRAL FORCES – MCQ - LEVEL – 2

CENTRAL FORCES – MSQ

CENTRAL FORCES – NAT – LEVEL – 1

CENTRAL FORCES – NAT – LEVEL – 2

UNIFORMLY ROTATING FRAME- CENTRIFUGAL AND CORIOLIS FORCES

Uniformly Rotating Frame

2 Topics

Uniformly Rotating Frame

Centrifugal Force

Circular Motion

5 Topics

Circular Motion

Centripetal Force

Banking of Roads

Effect of Earth Rotation on Apparent Weight

Problems on Circular Motion

1 Topic

Previous Years Questions on Coriolis forces

1 Topic

Previous Years Questions on coriolis forces

Quizzes on Circular Motion

5 Quizzes

CIRCULAR MOTION – MCQ - LEVEL – 1

CIRCULAR MOTION – MCQ - LEVEL – 2

CIRCULAR MOTION – MSQ

CIRCULAR MOTION – NAT - LEVEL – 1

CIRCULAR MOTION – NAT - LEVEL – 2

CONSERVATION LAWS

Law of Conservation of Linear Momentum

2 Topics

Conservation of Linear Momentum

Problems on Conservation of Linear Momentum

Law of Conservation of Energy

2 Topics

Conservation of Energy

Problems on Conservation of Energy

3 Topics

Problems on Collision

Oblique Collision

Quizzes on Work, Power and Energy

5 Quizzes

WORK, POWER AND ENERGY – MCQ - LEVEL – 1

WORK, POWER AND ENERGY – MCQ - LEVEL – 2

WORK, POWER AND ENERGY – MSQ

WORK, POWER AND ENERGY – NAT - LEVEL – 1

WORK, POWER AND ENERGY – NAT - LEVEL – 2

CENTRE OF MASS AND VRIABLE MASS SYSTEMS

5 Topics

Equation of Motion of Centre of Mass

Centre of Mass and Symmetry

Centre of Mass of Semi ring and Semi Disc

Problems on Centre of Mass

Variable Mass Systems

2 Topics

Problems on Variable Mass Systems

Quizzes on Centre of Mass

5 Quizzes

CENTRE OF MASS – MCQ - LEVEL – 1

CENTRE OF MASS – MCQ - LEVEL – 2

CENTRE OF MASS – MSQ

CENTRE OF MASS – NAT - LEVEL – 1

CENTRE OF MASS – NAT - LEVEL – 2

RIGID BODY DYNAMICS

Rotation about Fixed Axis

4 Topics

Moment of Inertia

Moment of Inertia of Famous Rigid Bodies

Rotation about Fixed axis

Translation + Rotation

6 Topics

Translation + Rotation

Problems on Rolling-1

Problems on Rolling – 2

Problems on Rolling-3

Problems on Rolling-4

Angular Momentum

4 Topics

Angular Momentum

Problems on Angular Momentum-1

Problems on Angular Momentum-2

Problems on Angular Momentum-3

Moment of Inertia Tensor

3 Topics

Moment of Inertia Tensor

Problems on Moment of Inertia Tensor

Rotational Kinetic Energy

Previous Year Problems on Rigid Body Dynamics in IISc

1 Topic

Previous Year Problems on Rigid Body Dynamics in IISc

Previous Year Problems on Rigid Body Dynamics in JEST

1 Topic

Previous Year Problems on Rigid Body Dynamics in JEST

Previous Year Problems on Rigid Body Dynamics in TIFR

1 Topic

Previous Year Problems on Rigid Body Dynamics in TIFR

Quizzes on Rigid Body Dynamics

5 Quizzes

RIGID BODY DYNAMICS – MCQ - LEVEL – 1

RIGID BODY DYNAMICS – MCQ - LEVEL – 2

RIGID BODY DYNAMICS – MSQ

RIGID BODY DYNAMICS – NAT - LEVEL – 2

RIGID BODY DYNAMICS – NAT – LEVEL – 1

FLUID DYNAMICS

6 Topics

Pressure in Fluid

Atmospheric Pressure

Archimedes Principle

Pressure Difference and Buoyant Force in Accelerating Fluids

Problems on Fluid Pressure and Buoyancy

4 Topics

Approach to Fluid Dynamics

Types of Fluid Flow

Equation of Continuity

Euler Equations and Its Applications

4 Topics

Euler Equation of Motion of Fluids

Bernoulli Equation

Problems on Bernoulli Principle

Thrust force in Fluid Systems

Quizzes on Fluid Dynamics

5 Quizzes

FLUID DYNAMICS – MCQ - LEVEL – 1

FLUID DYNAMICS – MCQ - LEVEL – 2

FLUID DYNAMICS – MSQ

FLUID DYNAMICS – NAT - LEVEL – 1

FLUID DYNAMICS – NAT - LEVEL – 2

COULOMB LAW AND ELECTRIC FIELD

3 Topics

Electric Field due to Rod

Electric Field due to Ring and Disc

2 Topics

Coulomb’s Law

Problems on Coulomb’s Law

Quizzes for Electric Field and Potential

4 Quizzes

ELECTRIC CHARGE MCQ LEVEL-1

ELECTRIC CHARGE MCQ LEVEL-2

ELECTRIC FIELD AND POTENTIAL–MCQ–LEVEL–1

ELECTRIC FIELD AND POTENTIAL–MCQ–LEVEL–2

GAUSS LAW OF ELECTROSTATICS AND APPLICATIONS

3 Topics

Electric Flux-contd

Determination of Charge Distribution on Conductors using Gauss Law

4 Topics

Charge on Conductors

Electric Field due to Infinite Conducting Sheet of Charge

Two Parallel Conducting Sheets of Charge

Three Parallel Conducting Sheet of Charge

Gauss Law of Electrostatics

7 Topics

Gauss Law of Electrostatics

Determination of Flux using Gauss Law

Determination of Electric Field using Gauss Law

Determination of Electric Field using Gauss Law-contd

Electric Field Inside Cavity

Electric Field due to Cylindrical Charge Distribution

Electric Field due to Infinite Non-conducting Sheet of Charge

Electrostatic Potential

2 Topics

Electrostatic Potential

Grounding of Conductor

Quizzes on Gauss law of Electrostatics

2 Quizzes

GAUSS LAW AND FIELD DUE TO CHARGE DISTRIBUTION–MCQ–LEVEL–1

ELECTRIC FLUX AND FIELD DUE TO CHARGE DISTRIBUTION—MCQ–LEVEL–2

3 Topics

Capacitance and Gauss Law

Spherical Plate Capacitor

Cylindrical Plate Capacitor

Force on Charged Surface

1 Topic

Force on Charged Surface

POLARIZATION OF DIELECTRICS

Polarization of Dielectrics

3 Topics

Electric Dipole

Polarization of Dielectric -1

Polarization of Dielectrics-2

Problems on Field Calculation

2 Topics

Problems on Field Calculation-1

Problems on Field Calculation-2

Boundary Condition of Polarization

1 Topic

Boundary Condition of Polarization

Problems on Calculation of Bound Charges

3 Topics

Problems on Calculation of Bound Charges-1

Problems on Calculation of Bound Charges-2

Problems on Calculation of Bound Charges-3

Boundary Condition of D and E

3 Topics

Boundary Condition of D and E

Problems on Boundary Conditions

Bound Charges at the interface of two Dielectrics

Effect of Polarization on Capacitance

2 Topics

Effect of Polarization on Capacitance

Quizzes on Polarization of Dielectrics

2 Quizzes

POLARISATION OF DIELECTRICS – MCQ LEVEL – 1

POLARISATION OF DIELECTRICS – MCQ LEVEL – 2

WORK AND ENERGY IN ELECTROSTATICS

Electrostatic Energy

4 Topics

Introduction to Work and Energy

Electrostatic Energy of System of Discrete Charges

Electrostatic Energy due to System of Continuous Distribution of Charges

Uniformly Charged Sphere and Spherical Shell

Problems on Electrostatic Energy

3 Topics

Problems on Electrostatic Energy-1

Electrostatic Energy for More than One Charge Distribution

Problems on Electrostatic Energy-2

Problems on Work and Energy

5 Topics

Problems on Work and Energy-1

Problems on Work and Energy-2

Problems on Work and Energy-3

Problems on Work and Energy-4

Problems on Work and Energy-5

Electrostatic Energy in Dielectrics

2 Topics

Electrostatic Energy in Dielectrics

Problems on Electrostatic Energy in Dielectrics

Quizzes on capacitance

5 Quizzes

CAPACITANCE (MCQ) – LEVEL – 1

CAPACITANCE–MCQ–LEVEL-2

CAPACITANCE–MSQ–LEVEL-2

CAPACITANCE–NAT–LEVEL-1

CAPACITANCE–NAT–LEVEL-2

BOUNDARY VALUE PROBLEMS

3 Topics

Series and Parallel Combination of Capacitors

Problems on Capacitors-1

Problems on Capacitors-2

Boundary Value Problems

3 Topics

Boundary Value Problems-1

Boundary Value Problems-2

Laplace Equation-properties

Uniqueness Theorems

2 Topics

First Uniqueness Theorem

Second Uniqueness Theorem

Laplace Equation in Spherical Polar Coordinates

3 Topics

Laplace Equation in Spherical Polar Coordinates

Dielectric Sphere in External Electric Field

Conducting Sphere in External Electric Field

Quizzes on Electrostatics

6 Quizzes

WORK AND ENERGY IN ELECTROSTATICS SYSTEM – MCQ LEVEL – 1

ELECTROSTATICS – MCQ LEVEL – 1

ELECTROSTATICS – MCQ – LEVEL – 2

ELECTROSTATICS – MSQ

ELECTROSTATICS – NAT LEVEL – 1

ELECTROSTATICS – NAT LEVEL – 2

CURRENT ELECTRICITY

Electric Current and Resistance

3 Topics

Electric Current

EMF and Potential Difference

Problems on Resistance

Combination of Resistors and Cells

2 Topics

Combination of Resistors

Wheatstone Bridge

Ammeter and Voltmeter

1 Topic

Ammeter and Voltmeter

Problems on Current Electricity

1 Topic

Problems on Current Electricity

Quizzes on Current Electricity

8 Quizzes

CURRENT ELECTRICITY – MCQ LEVEL-1

CURRENT ELECTRICITY–MSQ–LEVEL-2

CURRENT ELECTRICITY MCQ LEVEL-2

CURRENT ELECTRICITY MCQ LEVEL-3

CURRENT ELECTRICITY–MCQ–LEVEL-4

CURRENT ELECTRICITY–NAT–LEVEL-1

CURRENT ELECTRICITY (NAT)–LEVEL-2

CURRENT ELECTRICITY – MCQ LEVEL–5

MAGNETOSTATICS

Motion of Charged Particle in Magnetic Field

3 Topics

Motion of Charged Particle in Magnetic Field

Problems on Magnetic Force

Biot Savart Law

3 Topics

Biot Savart Law

Biot Savart Law-contd

Problems on Biot Savart Law

Gauss law of Magnetostatics

1 Topic

Gauss law of Magnetostatics

4 Topics

Problems on Ampere Law

Problems on Ampere Law-2

Solenoid and Toroid

Magnetic Dipoles and Force on Current Carrying Conductor

3 Topics

Force on Current Carrying Conductor

Magnetic Moment

Current Carrying Loop in External Magnetic Field

Quizzes on Magnetostatics

7 Quizzes

MAGNETOSTATICS–MCQ–LEVEL–1

MAGNETOSTATICS—MCQ—LEVEL–2

MAGNETIC EFFECT OF CURRENT– MCQ –LEVEL–1

MAGNETIC EFFECT OF CURRENT – MCQ LEVEL – 2

MAGNETIC EFFECT OF CURRENT – MSQ

MAGNETIC EFFECT OF CURRENT– NAT–LEVEL–1

MAGNETIC EFFECT OF CURRENT – NAT LEVEL – 2

FARADAY LAW OF ELECTROMAGNETIC INDUCTION

Faraday Law and Induced EMF

2 Topics

Types of Induced EMF

Problems on Faraday Law

5 Topics

Problems on Faraday Law-1

Problems on Faraday Law-2

Problems on Faraday Law-3

Problems on Faraday Law-4

Problems on Faraday Law-5

Quizzes on Faraday law

7 Quizzes

FARADAY'S LAW MCQ LEVEL-2

FARADAY’S LAW MCQ LEVEL-1

ELECTROMAGNETIC INDUCTION–MCQ–LEVEL-1

ELECTROMAGNETIC INDUCTION–MCQ–LEVEL-2

ELECTROMAGNETIC INDUCTION – MSQ

ELECTROMAGNETIC INDUCTION–NAT–LEVEL-1

ELECTROMAGNETIC INDUCTION–NAT–LEVEL-2

MAGNETIC MATERIALS

Magnetisation and H Vector

2 Topics

Boundary Conditions of B and H

2 Topics

Boundary Conditions of B

Boundary Conditions of H

1 Topic

Moving Coil Galvanometer

1 Topic

Moving Coil Galvanometer

DC CIRCUITS

Introduction to DC Circuit

1 Topic

Introduction to DC Circuit

5 Topics

2 Topics

Problems on LR Circuit

4 Topics

LC Circuit-contd

Problems on LC Circuit

Problems on LC Circuit-contd

1 Topic

AC CIRCUITS

6 Topics

Introduction to AC Circuit

Method of Complex Parameters

RC,LR and LC Circuit

Problems on AC Circuit

Quizzes on Alternating Current

5 Quizzes

ALTERNATING CURRENT–MCQ–LEVEL-1

ALTERNATING CURRENT–MCQ–LEVEL-2

ALTERNATING CURRENT–MSQ–LEVEL-2

ALTERNATING CURRENT–NAT–LEVEL-1

ALTERNATING CURRENT – NAT LEVEL – 2

MAXWELL EQUATIONS and poynting vector

Maxwell Equations

2 Topics

Maxwell Equations

Displacement Current

Poynting Vector

3 Topics

Poynting Vector

problems on Poynting Vector

Problems on Poynting Vector-contd

Quizzes on Maxwell Equation

2 Quizzes

MAXWELL’S EQUATION MCQ LEVEL-1

MAXWELL'S EQUATION MCQ LEVEL-2

ELECTROMAGNETIC WAVES

EM Waves in Free Space and Isotropic Dielectric Medium

2 Topics

EM Waves in Free Space

EM Waves in Isotropic Dielectric Medium

Problems on EM Waves

2 Topics

Problems on EM Waves-1

Problems on EM Waves-2

Quizzes on EM Waves

1 Quiz

PROPAGATION OF EM WAVES AND GAUGE TRANSFORMATION MCQ LEVEL-1

REFLECTION AND REFRACTION OF EM WAVES AT THE INTERFACE OF TWO DIELECTRICS

Kinematic Properties

3 Topics

Introduction to Kinematic Properties

Kinematic Properties

Derivation of Kinematic Properties

Fresnel Formula

4 Topics

Freshnel Formula

Fresnel Formula-contd

Analysis of Fresnel Formula

Reflection and Transmission Coefficient

Total Internal Reflection

2 Topics

Total Internal Reflection

Total Internal Reflection-contd

Section 3: MATHEMATICAL PHYSICS

Beta and Gamma Function

2 Topics

Beta and Gamma Function-1

Beta and Gamma Function-2

MULTIPLE INTEGRAL

Introduction to Double Integrals

1 Topic

Introduction to Double Integrals

Change of Order

7 Topics

Change of Order-1

Change of Order-2

Change of Order-3

Change of Order-4

Change of Order-5

Change of Order-6

Change of Order-7

2 Topics

Directional Derivative

Properties of Gradient

VECTOR CALCULUS

Tangent Plane and Normal

2 Topics

Tangent Plane and Normal

Problems on Tangent Plane and Normal

Problems on Gradient

1 Topic

Problems on Gradient

Divergence and Curl

4 Topics

Divergence and Curl

Problems on Divergence and Curl-1

Problems on Divergence and Curl-2

Problems on Divergence and Curl-3

4 Topics

Introduction to Line Integral

Problems on Line Integral-1

Problems on Line Integral-2

Problems on Line Integral-3

6 Topics

Introduction to Green’s Theorem

Problems on Green’s Theorem-1

Problems on Green’s Theorem-2

Problems on Green’s Theorem-3

Problems on Green’s Theorem-4

Problems on Green’s Theorem-5

Surface Integral

6 Topics

Introduction to Surface Integral

Problems on Surface Integral-1

Problems on Surface Integral-2

Problems on Surface Integral-3

Problems on Surface Integral-4

Problems on Surface Integral-5

Gauss Divergence Theorem

8 Topics

Introduction to Gauss Divergence Theorem

Problems on Gauss Divergence Theorem-1

Problems on Gauss Divergence Theorem-2

Problems on Gauss Divergence Theorem-3

Problems on Gauss Divergence Theorem-4

Problems on Gauss Divergence Theorem-5

Problems on Gauss Divergence Theorem-6

Problems on Gauss Divergence Theorem-7

5 Topics

Introduction to Stoke’s Theorem

Problems on Stoke’s Theorem-1

Problems on Stoke’s Theorem-2

Problems on Stoke’s Theorem-3

Problems on Stoke’s Theorem-4

Conservative Vector Field

3 Topics

Introduction to Conservative Vector Field

Problems on Conservative Vector Field-1

Problems on Conservative Vector Field-2

DIFFERENTIAL EQUATIONS

Introduction to Differential Equations

2 Topics

Order and Degree

Formation of Differential Equation

Differential Equation of First order and First Degree

8 Topics

Separation of Variables

Homogeneous Equation

Equation Reducible to Homogeneous Form

Exact Differential Equation

Integrating Factor

Integrating Factor-contd

Linear Differential Equation of first order

Equation reducible to Linear Form

Orthogonal Trajectory

2 Topics

Introduction to Orthogonal Trajectory

Problems on Orthogonal Trajectory

Differential Equation with Constant Coefficient

7 Topics

Introduction to Differential Equation with Constant Coefficient

Complementary Function

Particular Integral

Exponential Function

Trigonometric Function

Polynomial Function

Product of Exponential and other Function

Homogeneous Linear Differential Equation

4 Topics

Introduction to Homogeneous Linear Differential Equation

Problems on Cauchy Euler Equation-1

Problems on Euler Cauchy Equation-2

Equation reducible to cauchy Euler form

Differential Equation of Second Order

6 Topics

Introduction to Differential Equation of Second Order

Problems on Differential Equation of Second Order

Problems on Differential equation of second order-2

Variation of Parameters

Problems on Variation of parameters

Problems on Differential Equation of Second Order

MATRICES

Introduction to Matrices

7 Topics

Definition of Matrices

Types of Matrices

Operation on matrices

Operation on matrices-2

Transpose of matrix

Symmetric and Skew-symmetric matrices

Orthogonal matrices

3 Topics

Echelon Form of matrix

Problems on Rank

Linear Equations

6 Topics

Linear Equations

Homogeneous Linear equation

Homogeneous linear equation-contd

Non-homogeneous Linear Equation

Non-homogeneous Linear Equation-contd

Finding Inverse using elementary transformation

7 Topics

Introduction of Determinants

Properties of Determinants

Determinant Formula

Formula for Inverse of Matrix

Kramer’s Rule

Problems on Kramer’s Rule

Problems on Determinants

Revision of Matrices

6 Topics

Matrices- Revision

Problems on Rank

Elementary Matrix

Equivalence of matrix

Normal form of Matrix

3 Topics

Introduction to Vector Spaces

Subspaces associated with matrix

Linear Equations – Vector Space Approach

5 Topics

Homogeneous Linear Equations

Homogeneous Linear Equations-2

Homogeneous Linear Equations-3

Non-homogeneous Linear Equation

Non-homogeneous Linear Equation-2

Introduction to Eigenvalues and Eigenvectors

3 Topics

Introduction to Eigenvalues and Eigenvectors

Problems on Eigenvalues and Eigenvectors-1

Problems on Eigenvalues and Eigenvectors-2

Diagonalisation of Matrices and its Applications

5 Topics

Diagonalisation

Matrix Exponential

Differential Equations

Differential Equations-contd

Fibonaaci Sequence

Properties of Eigenvalues

1 Topic

Properties of Eigenvalues

Symmetric Matrices

3 Topics

Symmetric Matrices

Symmetric Matrices-2

Cayley Hamilton Equation

1 Topic

Cayley Hamilton Equation

Similar Matrices

1 Topic

Similar Matrices

5 Topics

Increasing and Decreasing Function

Problems on Monotonicity

Problems on Monotonicity-2

Problems on Monotonicity-3

DIFFERENTIAL CALCULUS

Critical Points

3 Topics

Critical and Stationary Points

Point of Inflexion

Problems on Point of Inflexion

Maxima and Minima

3 Topics

Local maxima and minima

Problems on local maxima and minima

Global maxima and minima

2 Topics

Problems on Rolle Theorem

Lagrange Mean Value Theorem

3 Topics

Introduction to Lagrange Mean Value Theorem

Problems on Lagrange Mean Value Theorem

Problems on Lagrange Mean Value Theorem-2

Taylors Theorem

2 Topics

Introduction to Taylor’s Theorem

Problems on Taylor’s Theorem

Function of Two Variables

7 Topics

Introduction to Function of Two Variables

limits of Function of Two Variables

Continuity of Function of Two Variables

Partial Derivatives

Diffrentiability of Function of Two Variables

Partial Derivatives of Higher Order

Homogeneous Function

1 Topic

Maxima and Minima of Function of Several Variables

2 Topics

Maxima and Minima of Function of two Variables

Maxima and Minima of Function of Several Variables

FOURIER SERIES

1 Topic

PARTICLE NATURE OF WAVE

Photoelectric Effect

3 Topics

Introduction to Quantum Mechanics

Photoelectric Effect

Problems on Photoelectric Effect

3 Topics

Problems on Compton Effect

Problems on Compton Effect-contd

Pair Production

2 Topics

Pair Production

Problems on Pair Annihilation

Cross-section of Photon Absorption and Scattering

1 Topic

Cross-section of Photon Absorption and Scattering

WAVE NATURE OF PARTICLE

Wave Nature of Particle

3 Topics

deBroglie Principle

Particle vs Waves

Indeterministic Nature of Quantum Systems

H ATOM

H atom and X-rays

1 Topic

H atom and X-rays

Quizzes on Origin of Quantum Mechanics

5 Quizzes

ORIGIN OF QUANTUM MECHANICS – MCQ- LEVEL – 1

ORIGIN OF QUANTUM MECHANICS–MCQ–LEVEL-2

ORIGIN OF QUANTUM MECHANICS (MSQ)

ORIGIN OF QUANTUM MECHANICS – NAT LEVEL – 1

ORIGIN OF QUANTUM MECHANICS NAT LEVEL–2

POSTULATES OF QUANTUM MECHANICS

Postulates of Quantum Mechanics

8 Topics

Postulates of Quantum Mechanics

Expectation Value

Uncertainty Relation

Complete Set of Commuting Operators

Time Evolution Operator

Schrodinger Wave Equation

Conservation of Probability

Time Evolution of Expectation Value

Problems on Postulates

3 Topics

Problems on Postulates-1

Problems on Postulates-2

Problems on Postulates-3

Quizzes on Postulates of Quantum Mechanics

3 Quizzes

POSTULATES OF QUANTUM MECHANICS–MCQ–LEVEL-1

POSTULATES OF QUANTUM MECHANICS (MCQ)–LEVEL-2

POSTULATES OF QUANTUM MECHANICS (NAT)–LEVEL-2

SCHRONDINGER WAVE WQUATION

Applications of Schrodinger Wave Equation

6 Topics

Applications of Schrodinger Wave Equation

Symmetric Potential and Parity

Particle in Infinite Potential Well

Particle in Finite Potential Well

Linear Harmonic Oscillator

1 Topic

Linear Harmonic Oscillator

Particle in Three Dimensional Box

1 Topic

Particle in Three Dimensional Box

Quizzes on Schrodinger Wave Equations

5 Quizzes

APPLICATION OF SCHRODINGER EQUATION – MCQ LEVEL – 2

APPLICATION OF SCHRODINGER WAVE EQUATION – MSQ

QUANTUM MECHANICS IN THREE DIMENSIONS (MCQ)–LEVEL–1

QUANTUM MECHANICS IN THREE DIMENSIONS – MSQ

QUANTUM MECHANICS IN THREE DIMENSIONS (NAT)–LEVEL–2

NUCLEAR PHYSICS

Basic Nuclear Properties and Radioactive Decay

5 Topics

Basic Nuclear Properties

Radioactive Decay

Problems on Radioactive Decay

2 Topics

Problems on Radioactive Decay

Problems on Radioactive Decay-contd

Quizzes on Nuclear Physics

5 Quizzes

NUCLEAR PHYSICS – MCQ LEVEL – 1

NUCLEAR PHYSICS (MCQ)–LEVEL–2

NUCLEAR PHYSICS (MSQ)

NUCLEAR PHYSICS (NAT)–LEVEL–1

NUCLEAR PHYSICS (NAT)–LEVEL–2

SPECIAL THEORY OF RELATIVITY

Einstein postulates

2 Topics

Pre-relativistic Notions

Einstein postulates

Time Dilation and Length Contraction

2 Topics

Length Contraction

Simultanity and Lorentz Transformation

2 Topics

Lorentz Transformation

Problems on Relativity

3 Topics

Problems on Relativity-1

Problems on Relativity-2

Problems on Relativity-3

Mass and Energy

2 Topics

Mass and Energy

Problems on Relativity-4

IISc Previous Year Problems on Relativity

1 Topic

IISc Previous Year Problems on Relativity

TIFR Previous Year Problems on Relativity

1 Topic

TIFR Previous Year Problems on Relativity

JEST Previous Year Problems on Relativity

1 Topic

JEST Previous Year Problems on Relativity

Quizzes on Special Theory of Relativity

3 Quizzes

SPECIAL THEORY OF REALATIVITY (MCQ)–LEVEL–1

SPECIAL THEORY OF REALATIVITY (MSQ)

SPECIAL THEORY OF REALATIVITY (NAT)–LEVEL–2

SIMPLE HARMONIC OSCILLATION

Simple Harmonic Motion

3 Topics

Oscillatory Motion

Restoring Force

Problems on Oscillation

Lissajous Figures

2 Topics

Lissajous Figures

Lissajous Figures-contd

Quizzes on Simple Harmonic Motion

4 Quizzes

SIMPLE HARMONIC MOTION–MCQ–LEVEL-1

SIMPLE HARMONIC MOTION–MSQ

SIMPLE HARMONIC MOTION–NAT–LEVEL-1

SIMPLE HARMONIC MOTION–NAT–LEVEL-2

DAMPED AND FORCED OSCILLATION

Damped Oscillation

3 Topics

Damped Oscillation-1

Damped Oscillation-2

Damped Oscillation-3

Forced Oscillation

4 Topics

Forced Oscillation-1

Forced Oscillation-2

Forced Oscillation-3

Forced Oscillation-4

WAVES

4 Topics

Traveling Waves

Classification of Waves

Superposition of Traveling Waves

Quizzes on Waves

5 Quizzes

WAVES – MCQ LEVEL – 1

WAVES – MCQ LEVEL – 2

WAVES – NAT LEVEL – 1

WAVES – NAT LEVEL – 2

GEOMETRICAL OPTICS

Fermat Principle

1 Topic

Fermat Principle

2 Topics

Thin Lens-contd

2 Topics

System of Lens-contd

INTERFERENCE

Young Double Slit Experiment

7 Topics

Young Double Slit Experiment

Problems on Young Double Slit

Shift in Fringes due to Introduction of Lamina

Problems on Double Slits-2

Problems on Double Slits-3

Problems on Double Slits-4

Fresnel Biprism

2 Topics

Problems on Thin Films

2 Topics

Newton’s Ring

Problems on Newton’s Ring

Quizzes on Interference

4 Quizzes

INTEFERENCE (MCQ)–LEVEL–1

INTERFERENCE – MCQ LEVEL – 2

INTERFERENCE– NAT LEVEL – 1

INTEFERENCE (NAT)–LEVEL–2

DIFFRACTION

2 Topics

Single Slit-contd

2 Topics

Double Slit-contd

Plane Transmission Grating

2 Topics

Plane Transmission Grating

Plane Transmission Grating-contd

Dispersive and Resolving Power

2 Topics

Dispersive and Resolving Power

Problems on Diffraction

Quizzes on Diffraction

2 Quizzes

DIFFRACTION – MCQ LEVEL – 1

DIFFRACTION – MCQ LEVEL – 2

POLARIZATION OF LIGHT

Brewster Law and Double Refraction

3 Topics

Plane Polarized Light

Double Refraction

Malus Law and Action of Half Wave and Quarter Wave Plate on Plane Polarized Light

3 Topics

Types of Uniaxial Crystals

Action of Half Wave and Quarter Wave Plate on Plane Polarized Light

Problems on Polarization of light

2 Topics

Problems on Polarization of light

Problems on Polarization of light-contd

Quizzes on Polarization

3 Quizzes

POLARIZATION (MCQ)–LEVEL–1

POLARIZATION (MSQ)

POLARIZATION (NAT)–LEVEL–2

THERMAL EXPANSION

Thermal Expansion

2 Topics

Thermal Expansion

Problems on Thermal Expansion

CALORIMETRY

4 Topics

Principle of Calorimetry

Problems on Calorimetry

TRANSMISSION OF HEAT

Thermal Conduction

2 Topics

Thermal Conduction

Series and Parallel Combination of Resistances

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Problems on Line Integral-3

IIT JAM PHYSICS Line Integral Problems on Line Integral-3

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Example 1 :

A particle moves counterclockwise along the curve $3x^2 + y^2 = 3$ from (1, 0) to a point P, under the action of the force

$\vec F\left( {x,y} \right) = \dfrac{x}{y}\hat i + \dfrac{y}{x}\hat j.$

Prove that there are two possible locations of P such that the work done by $\vec F$ is 1.

Solution :

$\dfrac{{{x^2}}}{1} + \dfrac{{{y^2}}}{3} = 1$

Point on ellipse is represented as

$(\cos \theta ,\sqrt 3 \sin \theta )$

$\int {\vec F \cdot d\vec r = \int {\left( {\dfrac{x}{y}\hat i + \dfrac{y}{x}\hat j} \right) \cdot (dx\hat i + dy\hat j)} }$

$\int {\vec F \cdot d\vec r = \int {\left( {\dfrac{x}{y}\hat i + \dfrac{y}{x}\hat j} \right) \cdot (dx\hat i + dy\hat j)} }$

$= \int {\dfrac{x}{y}dx + \dfrac{y}{x}dy}$

$= \int_0^\theta {\dfrac{{\cos \theta }}{{\sqrt 3 \sin \theta }}( - \sin \theta )d\theta } + \dfrac{{\sqrt 3 \sin \theta }}{{\cos \theta }} \cdot \sqrt 3 \cos \theta d\theta$

$= \int_0^\theta {\left( { - \dfrac{1}{{\sqrt 3 }}\cos \theta + 3\sin \theta } \right)d\theta }$

$= \left. { - \dfrac{1}{{\sqrt 3 }}\sin \theta - 3\cos \theta } \right|_0^\theta$

$= - \dfrac{1}{{\sqrt 3 }}\sin \theta - 3\cos \theta + 3$

Work done in equal to 1

So, ${1}{{\sqrt 3 }}\sin \theta - 3\cos \theta + 3 = 1$

$\Rightarrow \ \ \ \ \ \ \ \ \dfrac{1}{{\sqrt 3 }}\sin \theta + 3\cos \theta = 2$

$\Rightarrow \ \ \ \ \ \ \ \ {\left( {\dfrac{1}{{\sqrt 3 }}\sin \theta } \right)^2} = {(2 - 3\cos \theta )^2} \$

$\Rightarrow \ \ \ \ \ \ \ \ \dfrac{1}{3}{\sin ^2}\theta = 4 + 9{\cos ^2}\theta - 12\cos \theta \$

$\Rightarrow \ \ \ \ \ \ \ \ 28 \cos^2 \theta - 36 \cos \theta + 11 = 0$

$\Rightarrow \ \ \ \ \ \ \ \ (2 \cos \theta - 1)(14 \cos \theta - 11) = 0$

$\cos \theta = \dfrac{1}{2},\dfrac{{11}}{{14}}$

So, there are two value of $\theta$ i.e., two possible location of P such that the work done by $\vec F$ is 1.

Example 2 :

Find the circulation of the field

$\vec F = -{x^2}y\hat i + x{y^2}\hat j + ({y^3}-{x^3})\hat k$

around the curve C, where C is the intersection of the sphere $x^2 + y^2 + z^2 = 25$ and the plane z = 3. The orientation of the curve C is counterclockwise when viewed from above.

Solution :

$\vec F = -{x^2}y\hat i + x{y^2}\hat j + ({y^3}-{x^3})\hat k$

C is the curve of intersection of surfaces

$x^2 + y^2 + z^2 = 25, z = 3$

So, $x^2 + y^2 = 16$

$\vec F \cdot d\vec r = x^2ydx + xy^2dy + (y^3 - x^3)dz$

For curve C, z = 3, dz = 0

$\oint\limits_C {\vec F \cdot d\vec r = \int_C { - {x^2}ydx + x{y^2}dy} }$

Let $x = 4 \cos \theta, y = 4 \sin \theta$

$\oint\limits_C {\vec F} \cdot \,\,d\vec r\,\, = \,\,\int\limits_0^{2\pi } {(256{{\cos }^2}\theta {{\sin }^2}\theta d\theta } + \,256{\cos ^2}\theta {\sin ^2}\theta )d\theta$

$=512 \int\limits_0^{2\pi } {{{\sin }^2}} \theta {\cos ^2}\theta d\,\theta$

$= 512 \times 4\int\limits_0^{\pi /2} {{{\sin }^2}} \theta {\cos ^2}\theta \,d\,\theta$

$= 2048 \dfrac{\left \lceil 3/2 \right. \left \lceil \dfrac{3}{2} \right.}{2 \left \lceil 3 \right.} = 128 \pi$