(Please write your Roll No. immediately)

Roll No. ..................................

Time : 3 Hours

Maximum Marks : 75

Note : Attempt any 5 questions in all.

Q1

( a )

What is meant by the principle of superposition of waves? Explain in brief how it gives rise to the phenomenon of beats and stationary wave.

6

( b )

Is any loss of energy involved in either of these cases?

3

( c )

Plane harmonic waves of frequency 500sec^-1 are produced in air with displacement amplitude 1.00 x 10^-3 cm. Deduce (i) the pressure amplitude (ii) the energy density.

6

Q2

( a )

What is a satellite? Derive the formula for the orbital velocity and time period of a satellite.

8

( b )

Show that the velocity of escape of the body from the earth's surface is √2 times the velocity for a circular orbit just above the earth's surface.

7

Q3

( a )

For a driven oscillator of natural frequency ω/2π described by m x`` + r x` - k x = F sin ( p t ). Deduce an expression for velocity amplitude x_o. Show that for cases p>> ω, p= ω and p<< ω, this amplitude is governed by the inertia factor, the resistance factor and the spring factor respectively.

8

( b )

An under-damped harmonic oscillator has its amplitude reduced to 1/10^th of its initial value after 100 oscillations. If its time period be 1.15 sec., calculate (i) the damping constant (ii) the relaxation time.

7

Q4

( a )

Describe Michelson's- Interferometer and discuss the conditions for obtaining (i) circular fringes (ii) straight fringes with this interferometer.

5+5

( b )

Calculate the thickness of a double refracting plate capable of producing a path difference of λ/4 between extraordinary and ordinary waves.

5

Q5

( a )

Explain how a zone plate acts like a converging lens having multiple foci.

5

( b )

Define the terms (i) induced absorption (ii) spontaneous emission (iii) induced emission.

5

( c )

How induced emission explains Lasers?

5

Q6

( a )

Define the term expectation value of an observable quantity. Find the expectation values of (i) potential-energy (ii) linear momentum (iii) total energy.

8

( b )

Explain the construction and working of a Geiger-Muller counter. Discuss the significance of plateau curve in G.M. counter.

7

Q7

( a )

State and deduce mathematical expression for the law of addition of relativistic velocities. Show that in no case the resultant velocity of a material particle be greater than c.

6+3

( b )

A proton has a velocity equal to 0.999c in the laboratory. Find energy and momentum as observed in the same direction with velocity and momentum as observed in the same direction with velocity 0.999c w.r.t the laboratory. M_p=1.6725 x 10^-24 gm.

6

Q8

Write short notes on ANY THREE

3 x 5

(a)

Ruby laser

(b)

Central forces

(c)

Electron-Microscope

(d)

Reveberations