PH 3100 (PHYSICS FOR MATHEMATICS)

Date : 07-05-08 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

PART A (10 x 2 m= 20 m)

Draw graphs of kinetic and potential energies of simple harmonic motion as function of displacement.
State the theorem of parallel axes of moment of inertia.
State the Kepler’s laws of planetary motion.
What is gravitational red shift?
Define Poisson’s ratio.
List any two phenomena which bring out the surface tension of water.
Distinguish holonomic constraints from non-holonomic constraints.
Two photons travel in opposite direction. Find the relative velocity of one with respect to the other.
What are beats?
How is a stationary wave formed?

PART B (4 x 7 ½ m = 30 m)

ANSWER ANY FOUR QUESTIONS

Prove that a small oscillation of a liquid in a U-tube is simple harmonic.
(a)State and explain the principle of equivalence of general theory of relativity. (b)Explain any one experiment in support of general theory of gravitation.
Explain the torsional oscillation method of determining rigidity modulus of the material of a wire.
(a) Write down the Lorentz transformation equations (b) Determine the velocity of a particle whose kinetic energy is equal to its rest mass energy.
Determine the fundamental frequency and the first overtones of (i) open pipe and (ii) closed pipe

PART C (4 x 12 ½ m = 50 m)

ANSWRER ANY FOUR QUESTIONS

(a) Find the moment of inertia of a thin rod about an axis perpendicular to its length and passing through one of its ends.(b)Obtain an expression for acceleration of a body rolling down an inclined plane
(a) Determine the time period of an earth satellite which is orbiting near the surface of earth (b) Estimate the height of a geostationary satellite (c) What is escape velocity? Find an expression for it.
Obtain an expression for the volume rate of flow of a liquid through a capillary tube by Poiseuilles method.
Solve the problems of (i) Atwood’s machine and (ii) simple pendulum by Lagrangian dynamics
What is Doppler effect? Find expression for the apparent frequency in the case of (i) source moving towards stationary observer and (ii) observer moving towards stationary source.

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