Candidate may choose any optional subject from amongst the List of Optional Subjects given below:

Agriculture, Animal Husbandry and Veterinary Science, Anthropology, Botany, Chemistry, Civil Engineering, Commerce and Accountancy, Economics, Electrical Engineering, Geography, Geology, History, Law, Management, Mathematics, Mechanical Engineering, Medical Science, Philosophy, Physics, Political Science, and International Relations, Psychology, Public Administration, Sociology, Statistics, Zoology.

PHYSICS

PAPER-I

1. (a) Mechanics of Particles :

Laws of motion; conservation of energy and momentum, applications to rotating frames, centripetal and Coriolis accelerations; Motion under a central force; Conservation of angular momentum, Kepler’s laws; Fields and potentials; Gravitational field and potential due to spherical bodies, Gauss and Poisson equations, gravitational self-energy; Two-body problem; Reduced mass; Rutherford scattering; Centre of mass and laboratory reference frames.

(b) Mechanics of Rigid Bodies :

System of particles; Centre of mass, angular momentum, equations of motion; Conservation theorems for energy, momentum and angular momentum; Elastic and inelastic collisions; Rigid Body; Degrees  of freedom, Euler’s theorem, angular velocity, angular momentum,  moments  of  inertia,  theorems  of  parallel and perpendicular axes, equation of motion for rotation; Molecular rotations (as rigid bodies); Di and tri- atomic molecules; Precessional motion; top, gyroscope.

(c) Mechanics of Continuous Media :

Elasticity, Hooke’s law and elastic constants of isotropic solids and their inter-relation; Streamline (Laminar) flow, viscosity, Poiseuille’s equation, Bernoulli’s equation, Stokes’ law and applications.

(d) Special Relativity :

Michelson-Morely experiment and its implications; Lorentz transformations length contraction, time dilation, addition of relativistic velocities, aberration and Doppler effect, mass-energy relation, simple applications to a decay process. Four dimensional momentum vector; Covariance of equations of physics.

2. Waves and Optics :

(a) Waves :

Simple harmonic motion, damped oscillation, forced oscillation and resonance; Beats; Stationary waves in a string; Pulses and wave packets; Phase and group velocities; Reflection and refraction from Huygens’ principle.

(b) Geometrial Optics :

Laws of reflection and refraction from Fermat’s principle; Matrix method in paraxial optic-thin lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.

(c) Interference :

Interference of light -Young’s experiment, Newton’s rings, interference by thin films, Michelson interferometer; Multiple beam interference and Fabry Perot interferometer.

(d) Diffraction :

Fraunhofer diffraction - single slit, double slit, diffraction grating, resolving power; Diffraction by  a circular aperture and the Airy pattern; Fresnel diffraction: half-period zones and  zone  plates,  circular aperture.

(e) Polarisation and Modern Optics :

Production and detection of linearly  and circularly polarized light;  Double  refraction, quarter wave

plate; Optical activity; Principles of fibre optics, attenuation; Pulse dispersion in step index and parabolic index fibres; Material dispersion, single mode fibers; Lasers-Einstein A and B coefficients. Ruby and He-Ne lasers. Characteristics of laser light-spatial and temporal coherence; Focusing of laser beams. Three-level scheme for laser operation; Holography and simple applications.

3. Electricity and Magnetism :

(a) Electrostatics and Magnetostatics :

Laplace and Poisson equations in electrostatics and their applications; Energy of a system of charges, multipole expansion of scalar potential; Method of images and its applications. Potential and field due to a dipole, force and torque on a dipole in an external field; Dielectrics, polarisation. Solutions to boundary- value problems-conducting and dielectric spheres in a uniform electric field; Magnetic shell, uniformly magnetised sphere; Ferromagnetic materials, hysteresis, energy loss.

(b) Current Electricity :

Kirchhoff's laws and their applications. Biot-Savart law, Ampere’s law, Faraday’s law, Lenz’ law. Self- and mutual- inductances; Mean and rms values in AC circuits; DC and AC circuits with R, L and C components; Series and parallel resonance; Quality factor; Principle of transformer.

4. Electromagnetic Waves and Blackbody Radiation :

Displacement current and Maxwell’s equations; Wave equations in vacuum, Poynting theorem; Vector and scalar potentials; Electromagnetic field tensor, covariance of Maxwell’s equations; Wave equations in isotropic dielectrics, reflection and refraction at the boundary of two dielectrics; Fresnel’s relations; Total internal reflection; Normal and anomalous dispersion; Rayleigh scattering; Blackbody radiation  and Planck ’s radiation law- Stefan-Boltzmann law, Wien’s displacement law and Rayleigh-Jeans law.

5. Thermal and Statistical Physics :

(a) Thermodynamics :

Laws of thermodynamics, reversible  and  irreversible  processes,  entropy;  Isothermal,  adiabatic, isobaric, isochoric processes and entropy changes; Otto and Diesel engines, Gibbs’ phase rule and chemical potential; Van der Waals  equation of  state  of  a real gas,  critical constants;  Maxwell-Boltzmann  distribution of molecular velocities, transport phenomena, equipartition and virial theorems; Dulong-Petit, Einstein, and Debye’s theories of specific heat of solids; Maxwell relations and application; Clausius-Clapeyron equation. Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of gases.

(b) Statistical Physics :

Macro and micro states, statistical distributions, Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Distributions, applications to specific heat of gases and blackbody radiation; Concept of negative temperatures.