* Physics Vol I&II by David Haliday and Resnick (for basic concepts)
* Any practice book for objective questions.
* Any IIT/Engineering entrance type objective questions book in physics will do
* Mechanics – D.S. Mathur, B.S. Agarwal
* Waves and Oscillations – Brijlal & Subramanyam, B.S. Agarwal
* Optics – Brijlal& Subramanyam, B.S. Agarwal, Ajoy & Ghatak
* Thermal Physics – Singal, Agarwal & Prakash, B.S. Agarwal, Shah & Srivastava
* Electricity & Magnetism: D.C. TAyal, B.S. Agarwal, Griffith
* Any fundamental book on electrical engineering like B.L Thareja (Vol 1) or Vincent Del Tero
* Modern Physics – A Beiser (Concepts of modern physics), S.L. Gupta, B.S. Agarwal, J.B. Rajan
* Electronics – Milman & Halkias, S. Ramnam, Ryder or Bolstead, Malvina
* Properties of Matter – B. Aggarwal
* Atomic Physics – J. B. Rajan
* Fundamental of Magnetism electricity – B.N. Basudeva
* A Text Book of Suond – Khanna & Bedi
* Nuclear Physics – D.C. Tayal
* Introduction of Electrodynamics – Griffith
* Advanced Level Physics – Nelkon & Parkar
* University Physics – Zeemasky
* Numerical Problems – B. Lal & Subrahmanyam
* Quantum Mechnaics – A Ghatak
* A Dictionary of Physics – Goldstein

Paper 1

* Classical Mechnism -Gupta, Kumar & Sharma
- Takewale & Puranik
-H.Goldstein
* Mechanics – Kleppner & Kolenkov
-D.S. Mathur
* Wave/Spl.Relatively – D.S. Mathur/Kleppner&Kolenkov
* Special Relativity-R.Resnic
-Gupta & Goyal
* Optics-Ajay Ghatak
-B.S. Agarwal
* Electrodyanamics – David Griffiths
* EM Theory -Chopra&Agarwal/Satya Prakash
* Thermal Physics – P.K Chakraborty
- Satya Prakash, Singhal & Agarawal
-Statistical Physics -B.B laud

Paper 2

* Quantum Physics- Resnick & Eisberg
* Concept of Mordern Physics – Arthut Bevser
* Quantum Mechanics -Ghatak & Loknathan
-Chatwal & Anand/Satya Prakash
* Atomic & Molecular Spectra -Rajkumar
* Nuclear Physics -S.B Patel
* Solid State Physics -Kittel
* Electronics -Allon Mottershed
* Objective Physics -H.C. Verma/TMH

Instructions

Answers must be written in the medium specified in the Admission Certificate issued to you, which must be stated clearly on the cover of the answer book in the space provided for the purpose. No marks will be given for the answers written in a medium other than that specified in the Admission Certificate.

Candidates should attempt Questions 1 and 5 which are compulsory, and any three of the remaining questions selecting at least one question from each section.

Assume suitable data if considered necessary and indicate the same clearly.

All questions carry equal marks.

SECTION A.

1. Answer any three of the following:

(a) Using the rocket equation and its integral find the final velocity of a single stage rocket. Given that (i) the velocity of the escaping gas is 2500 m/s, (ii) the rate of loss of mass is. (where m0) is the initial mass and 0.27 m0 is the final mass).

(b) Two spaceships are moving at a velocity of 0.9 c relative to the Earth in opposite directions. What is the speed of one spaceship relative to the other? (c = velocity of light)

(c) A wave is represented by – Find wavelength , velocity v, frequency f and the direction of propagation. If it interferes with another was given , find the amplitude and the phase of the resultant wave (All dimensions are in SI system).

(d) Derive the expression for resolving power of a diffraction grating with N lines. Calculate the minimum number of lines in the diffraction grating if it has to resolve the yellow lines of sodium (589.0 nm and 589.6 nm) in the first order.

2. (a) Using the Lagrangian for the system of a planet and the Sun obtain the equation of motion. Use them to get the equations for the orbit.

(b) Derive the relationship between the impact parameter and the scattering angle for the scattering of an particle of charge +2e by a nucleus of charge +Ze. Calculate the impact parameter for an angle of deflection of 30o if the kinetic energy of the alpha particle is 6×10-13 J.

3. (a) State Fermat’s principle. Apply it to get the laws of reflection from a plane surface.

(b) The phase velocity of the surface wave in a liquid of surface tension T and density is given by . Show that the group velocity vg of the surface wave is given by

3. (c) An observer A sees two events at the same space point () and separated in time by t=10-6 s. Another observer B sees them to be separated t’ = 3×10-6 s. What is the separation in space of the tow events as observed by B? What is the speed of B relative to A?

4. (a) How do you know that the light is a transverse wave? What is a quarter wave plate? How is it constructed?

(b) Discuss the Fresnel diffraction pattern formed by a straight edge using the Cornu’s spiral.

(c) In an experiment using a Michelson interferometer, explain with the help of suitable ray diagrams

(i) Why do we need extended source of light,

(ii) Why do we get circular fringes, and

(iii) Shifting of fringes inwards or outwards as we shift the movable mirror.

SECTION B

5. Solve any three of the following:

5. (a). Calculate the electric field for a point on the axis of a uniform ring of a charge ‘q’ and radis a. Where does the maximum value occur.

(b) Show that the potential energy of a charge Q uniformly distributed throughout the sphere of radius R is give by .

(c) Describe Carnot cycle and show that efficiency is given by , where the symbols have their usual meaning.

(d) Derive the Bose-Einsten distribution for an ideal gas.

6. (a) Using Kirchoff’s laws find currents in each branch of the circuit shown in the following diagram.

(b) A Geiger tube consists of a wire a wire of radius 0.2 mm and length 12 cm and a co-axial metallic cylinder of radius 1.5 cm and length 12 cm. Find

(i) the capacitance of the system, and

(ii) the charge per unit length of the wire when the potential difference between the wire and the cylinder is 1.2 kV.

(c) A series LCR circuit with L = 2 H, C = 2 F and R = 20 ohm is powered by a source of 100 volts and variable frequency. Find

(i) the resonance frequency, fo,

(ii) the value of Q

(iii) the width of resonance f and

(iv) the maximum current at resonance.

7. (a) Why did Maxwell have to introduce the idea of displacement current? Derive the wave equation from Maxwell’s laws. Obtain Fresnel’s formula for reflection and transmission coefficients of the electric vector when it is perpendicular to the plane of incidence.

(b) What are vector and scalar potentials for the electromagnetic field? Are they unique? Explain what are Coulomb’s and Lorentz gauges. Derive the electromagnetic wave equation in Lorentz gauge and show that it is equivalent to Maxwell’s equation.

8.(a) Discuss the phenomenon of Bose-Einstein condensation. Obtain the expression for the condensation temperature. Briefly comment on observation of Bose-Einstein condensate.

(b) A bulb filament is constructed from a tungsten wire of length 2 cm and diameter 50 m. It is enclosed in a vacuum bulb. What temperature does it reach when it is operated at a power of 1 watt? Given:

(i) Emissivity of tungsten = 0.4

(ii) Stefan’s constant = 5.67×10-8 watt/m2K4.

Physics  Syllabus for Preliminary Examination

1. Mechanics and Waves
Dimensional analysis. Newtons laws of motion and applications, variable mass systems, projectiles. Rotational dynamics-kinetic energy, angular momentum, theorems of moment of intertia and calculations in simple cases. Conservative forces, frictional forces. Gravitaional potential and intensity due to spherical objects. Central forces, Keplers problem, escape velocity and artificial satellites (including GPS). Streamline motion, viscosity, Poiseuilles equation. Applications of Bernoullis equation and Stokes law.
Special relativity and Lorentz transformation-length contraction, time dilation, mass-energy relation.
Simple harmonic motion, Lissajous figures. Damped oscillation, forced oscillation and resonance. Beats, Phase and group velocities. Stationary waves, vibration of strings and air columns, longitudinal waves in solids. Doppler effect. Ultrasonics and applications.

2. Geometrical and Physical Optics.
Laws of reflection and refraction from Fermats principle. Matrix method in paraxial optics- thin lens formula, nodal planes, system of two thin lenses. Chromatic and spherical aberrations. Simple optical instruments-magnifier, eyepieces, telescopes and microscopes.
Huygens principle-reflection and refraction of waves. Interference of light-Youngs experiment, Newtons rings, interference by thin films, Michelson interferometer. Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power. Fresnel diffraction-half-period zones and zone plate. Production and detection of linearly, circularly and elliptically polarised light. Double refraction, quarter-waves plates and half-wave plates. Polarizing sheets. Optical activity and applications. Rayleigh scattering and applications.
Elements of fibre optics-attenuation; pulse dispersion in step index and parabolic index fibres; material dispersion. Lasers, characteristics of laser light-spatial and temporal coherence. Focussing of laser beams and applciations.

3. Heat and Thermodynamics
Thermal equilibrium and temperature. The zeroth law of thermodynamics. Heat and the first law of thermodynamics. Efficiency of Carnot engines. Entropy and the second law of thermodynamics. Kinetic theory and the equation of state of an ideal gas. Mean free path, distribution of molecular speeds and energies. Trasport phenomena. Andrews experiements-van der Waals equation and applications. Joule-Kelvin effect and applications. Brownian motion. Thermodynamic potentials-Maxwell relations. Phase transitions. Kirchhoffs laws. Black-body radiation-Stefan-Boltzmann law, spectral radiancy, Wien displacement law, application to the cosmic microwave background radiation, Planck radiation law.

4. Electricity and Magnetism
Electric charge, Coulombs law, electric field, Gauss law. Electric potential, van de Graff accelerator. Capacitors, dielectrics and polarization. Ohms law, Kirchhoffs first and second rules, resistors in series and parallel, applications to two-loop circuits. Magnietic field-Gausslaw for magnetism, atomic and nuclear magnetism, magnetic susceptibility, classification of magnetic materials. Cirulating charges, cyclotron, synchrotron. Hall effect. Biot-Savart law, Amperes law, Faradays law of induction., Lenzs law. Inductance. Alternating current circuits-RC, LR, single-loop LRC circuits, impedance, resonance, power in AC circuits. Displacement current, Maxwells equations (MKS units), electromagnetic waves, energy transport and Poynting vector.

5. Atomic and Nuclear Physics
Photoelectric effect, Einsteins photon theory. Bohrs theory of hydrogen atom. Stern-Gerlach experiment, quantisation of angular momentum, electron spin. Pauli exclusion principle and applications. Zeeman effect. X-ray spectrum, Braggs law, Bohrs theory of the Mosley plot. Compton effect, Compton wavelength. Wave nature of matter, de Broglie wavelength, wave-particle duality. Heisenbergs uncertainty relationships. Schroedingers equation-eigenvalues and eigenfunctions of (i) particle in a box, (ii) simple harmonic oscillator and (iii) hydrogen atom. Potential step and barrier penetration. Natural and artificial radioactivity. Binding energy of nuclei, nuclear fission and fusion. Classification of elementary particles and their interactions.

6. Electronics
Diodes in half-waves and full-wave rectification, qualitative ideas of semiconductors, p type and n type semiconductors, junction diode, Zener diode, transistors, binary numbers, Logic gates and truth tables, Elements of microprocessors and computers. Physics (Optional) Syllabus for Main Examination

Paper-I
Section-A

1. Classical Mechanics
(a) Particle dynamics
Centre of mass and laboratory coordinates, conservation of linear and angular momentum. The rocket equation. Rutherford scattering, Galilean transformation, intertial and non-inertial frames, rotating frames, centrifugal and Coriolis forces, Foucault pendulum.
(b) System of particles
Constraints, degrees of freedom, generalised coordinates and momenta. Lagranges equation and applications to linear harmonic oscillator, simple pendulum and central force problems. Cyclic coordinates, Hamilitonian Lagranges equation from Hamiltons principle.
(c) Rigid body dynamics
Eulerian angles, inertia tensor, principal moments of inertia. Eulers equation of motion of a rigid body, force-free motion of a rigid body. Gyroscope.
2. Special Relativity, Waves & Geometrical Optics
(a) Special Relativity
Michelson-Morley experiment and its implications. Lorentz transformations-length contraction, time dilation, addition of velocities, aberration and Doppler effect, mass-energy relation, simple applications to a decay process. Minkowski diagram, four dimensional momentum vector. Covariance of equations of physics.
(b) 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.
(c) Geometrical Optics
Laws of relfection and refraction from Fermats principle. Matrix method in paraxial optic-thin lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.
3. Physical Optics
(a) Interference
Interference of light-Youngs experiment, Newtons rings, interference by thin films, Michelson interferometer. Multiple beam interference and Fabry-Perot interferometer. Holography and simple applications.
(b) Diffraction
Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power. Fresnel diffraction: – half-period zones and zones plates. Fresnel integrals. Application of Cornus spiral to the analysis of diffraction at a straight edge and by a long narrow slit. Diffraction by a circular aperture and the Airy pattern.
(c) Polarisation and Modern Optics
Production and detection of linearly and circularly polarised 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 fibres. Lasers-Einstein A and B coefficients. Ruby and He-Ne lasers. Characteristics of laser light-spatial and temporal coherence. Focussing of laser beams. Three-level scheme for laser operation.

Section-B
4. Electricity and Magnetism
(a) Electrostatics and Magnetostatics
Laplace ad 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 bounary-value problems-conducting and dielectric spheres in a uniform electric field. Magentic shell, uniformly magnetised sphere. Ferromagnetic materials, hysteresis, energy loss.
(b) Current Electricity
Kirchhoffs laws and their applications. Biot-Savart law, Amperes law, Faradays law, Lenz law. Self-and mutual-inductances. Mean and rms values in AC circuits. LR CR and LCR circuits- series and parallel resonance. Quality factor. Principal of transformer.
5. Electromagnetic Theory & Black Body Radiation
(a) Electromagnetic Theory
Displacement current and Maxwells equatons. Wave equations in vacuum, Poynting theorem. Vector and scalar potentials. Gauge invariance, Lorentz and Coulomb gauges. Electromagnetic field tensor, covariance of Maxwells equations. Wave equations in isotropic dielectrics, reflection and refraction at the boundary of two dielectrics. Fresnels relations. Normal and anomalous dispersion. Rayleigh scattering.
(b) Blackbody radiation
Balckbody radiation and Planck radiation law- Stefan-Boltzmann law, Wien displacement law and Rayleigh-Jeans law. Planck mass, Planck length, Planck time,. Planck temperature and Planck energy.
6. Thermal and Statistical Physics
(a) Thremodynamics
Laws of thermodynamics, reversible and irreversible processes, entropy. Isothermal, adiabatic, isobaric, isochoric processes and entropy change. Otto and Diesel engines, Gibbs phase rule and chemical potential. van der Waals equation of state of a real gas, critical constants. Maxwell-Boltzman distribution of molecular velocities, transport phenomena, equipartition and virial theorems. Dulong-Petit, Einstein, and Debyes theories of specific heat of solids. Maxwell relations and applications. Clausius- Clapeyron equation. Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of gases.
(b) Statistical Physics
Saha ionization formula. Bose-Einstein condenssation. Thermodynamic behaviour of an ideal Fermi gas, Chandrasekhar limit, elementary ideas about neutron stars and pulsars. Brownian motion as a random walk, diffusion process. Concept of negative temperatures.

Paper-II
Section-A

1. Quantum Mechanics I
Wave-particle dualitiy. Schroedinger equation and expectation values. Uncertainty principle. Solutions of the one-dimensional Schroedinger equation free particle (Gaussian wave-packet), particle in a box, particle in a finite well, linear harmonic oscillator. Reflection and transmission by a potential step and by a rectangular barrier. Use of WKB formula for the life-time calcuation in the alpha-decay problem.
2. Quantum Mechanics II & Atomic Physics
(a) Quantum Mechanics II
Particle in a three dimensional box, density of states, free electron theory of metals. The angular meomentum problem. The hydrogen atom. The spin half problem and properties of Pauli spin matrices.
(b) Atomic Physics
Stern-Gerlack experiment, electron spin, fine structure of hydrogen atom. L-S coupling, J-J coupling. Spectroscopic notation of atomic states. Zeeman effect. Frank-Condon principle and applications.
3. Molecular Physics
Elementary theory of rotational, vibratonal and electronic spectra of diatomic molecules. Raman effect and molecular structure. Laser Raman spectroscopy Importance of neutral hydrogen atom, molecular hydrogen and molecular hydrogen ion in astronomy Fluorescence and Phosphorescence. Elementary theory and applications of NMR. Elementary ideas about Lamb shift and its significance.

Section-B
4. Nuclear Physics
Basic nuclear properties-size, binding energy, angular momentum, parity, magnetic moment. Semi-empirical mass formula and applications. Mass parabolas. Ground state of a deuteron magnetic moment and non-central forces. Meson theory of nuclear forces. Salient features of nuclear forces. Shell model of the nucleus-success and limitations. Violation of parity in beta decay. Gamma decay and internal conversion. Elementary ideas about Mossbauer spectroscopy. Q-value of nuclear reactions. Nuclear fission and fusion, energy production in stars. Nuclear reactors.
5. Particle Physics & Solid State Physics
(a) Particle Physics
Classification of elementary particles and their interactions. Conservation laws. Quark structure of hadrons. Field quanta of electroweak and strong interactions. Elementary ideas about Unification of Forces. Physics of neutrinos.
(b) Solid State Physics
Cubic crystal structure. Band theory of solids- conductors, insulators and semiconductors. Elements of superconductivity, Meissner effect, Josephson junctions and applications. Elementary ideas about high temperature superconductivity.
6. Electronics
Intrinsic and extrinsic semiconductors-p-n-p and n-p-n transistors.Amplifiers and oscillators. Op-amps. FET, JFET and MOSFET. Digital electronics-Boolean identities, De Morgans laws, Logic gates and truth tables., Simple logic circuits. Thermistors, solar cells. Fundamentals of microprocessors and digital computers.