Express angular momentum in terms of kinetic, potential and total energy of a satellite of mass m in a circular orbit of radius r. Describe Michelson-Morley experiment and show how the negative results obtained from this experiment were interpreted. Sunlight is reflected from a calm lake. The reflected light is 100% polarized at a certain instant. What is the angle between the sun and horizon? Explain with proper example the interferences due to 'division of wavefront' and 'division of amplitude'.

(e) Find the velocity of sound in a gas in which two waves of wavelengths 1.00 m and 1·01 m produce 10 beats in 3 seconds.

2.(a) Define moment of inertia and explain its physical significance. Calculate the moment of inertia of an annular ring about an axis passing through its centre and perpendicular to its plane.
A diatomic molecule can be considered to be made up of two masses m1 and m2 separated by a fixed distance r. Derive a formula for the distance of centre of mass, from mass Also show that the moment of inertia about an axis through C and perpendicular to r is J.Lr 2 where J.L m1m2/m1 m2
State and explain Stokes' law. A drop of water of radius 0·01 m is falling through a medium whose density is 1·21 kg/m^3 and n=1.8x10^-5 N-s/m^2.Find the terminal velocity of the drop of water.

3.(a) What is multiple-beam interference? Discuss the advantages of multiple-beam interferometry over two-beam interferometry. Explain the fringes formed by Fabry-Perot interferometer.

(b) Show that the areas of all the half-period zones are nearly the same. Find the radius of 1st half-period zone in a zone plate whose focal length is 50 cm and the wavelength of the incident light is 500 nm.

(c) A plane-polarized light passes through a double-refracting crystal of thickness 40 Mm and emerges out as circularly polarized. If the birefringence of the crystal is 0·00004, then find the wavelength of the incident light.

(d) Obtain the system matrix for a thin lens placed in air and made of material of refractive index 1.5 having radius of curvature 50 cm each. Also find its focal length.

4.(a) A ball moving with a speed of 9 m/s strikes an identical stationary ball such that after the collision the direction of each ball makes an angle 30 with the original line of motion. Find the speed of the balls after the collision. Is the kinetic energy conserved in this collision?

(b) Prove that x^2 y^2 z^2 c^2 t^2 is invariant under Lorentz transformation.

(c) How is laser light different from ordinary light? Discuss the working principle of ruby laser. What role do chromium ions play in this process? Explain the principle of operation of optical fibre. What are the different losses that take place in optical fibre?

5.(a) Discuss the principle of 'artificial dielectric'. Where do you find its use?
How large an inductance needs to be connected in series with a 120 60 W lightbulb if it is to operate normally when the combination is connected across a 240 60 Hz supply? A charge q MC is placed at a =10 cm from an infinite grounded conducting plane sheet. Find the

(i) total charge induced on the sheet.

(ii) force on the charge q and

(iii) total work required to remove the charge slowly to an infinite distance from the plane.

(d) 1 litre of hydrogen at 127°C and 10^6 dynes/cm^2 pressure expands isothermally until its volume is doubled and then expands adiabatically until its volume is redoubled. Calculate the resulting pressure. Using the Maxwell-Boltzmann distribution law, show that there cannot be any negative absolute temperature.

6.(a) When a person carrying something metallic walks through the doorway of a metal detector, it emits a sound. Explain the reason behind it.
A 200 ohm resistor and a 15 MF capacitor are connected in series to 220 50 Hz a.c. supply. Calculate the current in the circuit and the r.m.S. voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the supply voltage? If yes, resolve the paradox. Write down Stefan-Boltzmann law of radiation and derive it from Planck's law of radiation.
An aluminium foil of relative emittance O·1 is placed between two concentric spheres (assumed perfectly black) at temperatures 300 K and 200 K respectively. Find the temperature of the foil once the steady state is reached. Write down the electromagnetic wave equations in non-conducting dielectric medium. Hence show that the velocity of wave propagation is given by v where the symbols have their usual meanings. A current )MA charges up a 120 nF capacitor for a period of 2 seconds. If the final voltage across the capacitor is 15 what was the initial, voltage across it? Why does a soap bubble expand upon electrification?
A sphere of radius R contains a charge Q and a charge distributed uniformly in the upper and lower hemispheres respectively. Show that the dipole moment of charge distribution is 3/4 QRk. where k is directed along4 the polar axis of the spherical coordinate system.
Discuss briefly the features of 'guard rings'.
The plates of a capacitor are square-shaped, each of side l. The plates are inclined at an angle a. to each other. The smallest distance between the plates is a. Calculate the capacitance when a. is small. Write down the physical significance of Maxwell's equations and explain the concept of displacement current by using a proper example. Derive Clausius-Clapeyron equation. How does it explain the effect of pressure on melting point of solids and boiling point of liquids?

8.(a) Write and explain the Maxwell-Boltzmann distribution. Using this distribution, find the expressions for the most probable speed, mean speed and root-mean-square speed. Calculate the critical temperature for helium, given the values for critical constants, a =6.15 X b =9·95 x where the unit of pressure is atm and the sample is kept at NTP. A reversible engine converts 1/6 of the heat input into work. When the temperature of the sink is reduced by 62°C, its efficiency is doubled. Find the temperatures of source and sink.
Explain Bose-Einstein distribution and obtain the same from the grand canonical ensemble.