PAPER 1

QUESTION 2: a) State and prove Stoke's Theorem
b) Prove that if the vector is a gradient of a scalar function then its line integral around a closed curve is zero.
c) A particle moving along a curve x=2t^2, y= t^2 - 4t, z= 3t-5 where t is the time. Find the components of its velocity and acceleration at time t=1 in the direction 2i-3j+2k.


QUESTION 3: a) What is moment of inertia? State and prove parallel axis theorem.
b) Calculate rotational inertia of a hollow cylinder about cylindrical axis.

QUESTION 4: a) State and prove the Kepler's Laws of areas and Periods of planetary motion.

b) A satellite orbits at a height of 230km above the earth. What is the period of the satellite?

c) At what altitude above the earth surface the value of 'g' is three-quarters of its value at the surface of the earth.

QUESTION 5: a) What is diffraction grating? Explain how grating diffracts light? Derive relation for resolving power of grating.
b) What is meant by polarization of light? How can we get a plane-polarized light by a polarizing sheet?

QUESTION 6: a) Derive equation of Lorentz velocity transformations and show that the speed of light is independent of the relative motion between the frames of reference.
b) The siren of the police car emits a source tone at a frequency of 1125 Hz. Find the frequency that you receive in your car under the following circumstances.
i) Your car is at rest, police car moving towards you at 29 m/s.
ii) Police car at rest, your car moving towards it at 29 m/s.
iii) Your and police car are moving towards one another at 14.5 m/s
iv) Your car moving at 9 m/s, police car chasing behind you at 38 m/s.

QUESTION 7: a) Define Entropy. State Second Law of Thermodynamics in terms of Entropy.
b) Discuss applications of the first Law of Thermodynamics.
c) discuss briefly the Lissajous patterns

QUESTION 8: Explain any FOUR of the following:

a) Doppler's Effect
b) Bernoulli's Theorem
c) Newton's Rings
d) He-Ne Gas LASER
e) Brownian Motion