PHYSICS

PAPER–I — 100 Marks

I. Mechanics, Vectors and Relativity

• Vectors: Dot, cross and triple products; gradient; divergence and their applications.

• Newtonian Mechanics: Newton’s laws of motion; calculus-based approach to kinematics, forces and dynamics.

• Conservation Laws: Conservation of energy; conservation of linear and angular momentum.

• Rigid Body Dynamics: Dynamics of rigid bodies; spin and precession; gyroscope.

• Gravitation: Gravitation; planetary motion and satellites; Kepler’s laws; centripetal forces.

• Special Theory of Relativity: Michelson–Morley experiment and Einstein’s postulates; Lorentz transformation; time dilation and length contraction; equivalence of mass and energy.

II. Fluid Mechanics

• Surface tension

• Viscosity

• Elasticity

• Fluid motion

• Bernoulli’s theorem

III. Waves and Oscillations

• Free oscillations with one and two degrees of freedom

• Forced and damped oscillations

• Phenomenon of resonance

• Simple harmonic motion

• Travelling waves and transmission of energy

• Phase and group velocity

• Standing waves

• Basics of sound waves

• Reflection, refraction, interference, diffraction and polarization of waves

• Interferometer and Newton’s rings

• Diffraction gratings and their resolving power

• Spectrometers

• Electromagnetic wave equation

• Normal and anomalous dispersion

• Coherence

• Lasers and their applications

IV. Heat and Thermodynamics

• Perfect gas and Van der Waals equation

• Three laws of thermodynamics

• Internal energy, temperature and entropy

• Thermal properties of simple systems

• Production and measurement of low temperatures

• Kinetic theory of gases

• Maxwellian distribution of molecular velocities

• Brownian motion

• Transport phenomena

• Classical Maxwell–Boltzmann statistics and its applications

• Quantum Bose–Einstein and Fermi–Dirac statistics

PAPER–II — 100 Marks

I. Electricity and Magnetism

• Electric field due to point charges

• Gauss’s law

• Electric potential

• Poisson’s and Laplace’s equations

• Dielectric medium and polarization

• Capacitance

• Moving charges and the resulting magnetic field

• Ampere’s law

• Vector potential

• Magnetic properties of matter

• Transient current

• Faraday’s law of electromagnetic induction

• Alternating current and LCR circuit

• Maxwell’s equations

• Poynting theorem and Poynting vector

• Maxwell’s equations in integral and differential forms

II. Modern and Quantum Physics

• Operators and quantum states

• Observables

• Time-dependent and time-independent Schrödinger equations

• Angular momentum

• Spin-½ particle in a magnetic field

• Wave mechanics

• Particle in a box

• Quantum tunnelling

• One-dimensional harmonic oscillator

• Heisenberg’s uncertainty relationship and indeterminacy based on commutation properties of operators

• Bohr theory and quantum numbers, including electron spin

• Pauli’s exclusion principle

• Spectra of simple systems with one or two valence electrons

• Photoelectric effect

• Compton scattering

• Pair production

• Lande’s g-factor

• Zeeman effect

• Raman effect

• Waves and particles

• De Broglie’s hypothesis

III. Solid State Physics

• Crystal lattice and structure

• Bravais lattice

• Free electron model

• Band theory and electrons in a periodic potential

• Fermi energy and density of states

• n-type and p-type semiconductors

• Physics of the transistor and MOSFET

• Dielectric properties

• Magnetic properties and origin of magnetism

IV. Nuclear Physics

• Structure of nuclei

• Radioactivity: α, β and γ decay

• Methods of detection

• Mass spectrometer

• Accelerators

• Phenomenon of fission

• Nuclear reactors and nuclear power

• Nuclear fusion and its applications

• Elementary particles and their properties

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