LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – MATHEMATICS

FOURTH SEMESTER – APRIL 2012

MT 4813 – RELATIVISTIC MECHANICS

 

 

Date : 23-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

Answer ALL the questions and each question carries 20 marks.

 

1. a. i.what is Relativity?

ii..Explain the meaning of  absolute quantities with examples.

iii..Is relativistic energy is absolute constant?

1.      Explain why Michelson-Morley experiment should be repeated during nights and days and

during  all seasons of the year?

1.       What do you understand by Relativistic effects?

OR

1. i. What is the rest frame of a moving body?

ii .If two events are simultaneous in a reference frame S, will they also be simultaneous in another

reference frame S’ moving with constant velocity relative to S ?

iii. If velocity of light in a frame S is v = c, what will be the velocity of light in the frame S’.

1. What is the rest mass of a light photon?
2. What types of energies are included in E= mc² ?

-6 marks

1. c. Derive the Lorentz Transformations

OR

1. d. i. Define Aberration and determine the relativistic value of Aberration and deduce its

classical value.

1. Discuss about Doppler’s effect.                                                                            –14marks

 

02 .a. Derive the transformation formula for force.

 

OR

1. Derive the relativistic equations of motion and energy.           -6 marks

 

1. c. Discuss the concept of Minkowski space and Space-like and Time-like intervals.

OR

1. i.Prove that  is invariant under Lorentz transformation.

ii.If a moving particle has velocities u and u’ in the frame S and S’ respectively. Prove that

-14marks

 

3.a.                                                                                                        OR

1. If B_ij = A _i,j – A _j,i, prove that B _ij,k +B _jk,i + B _ki,j = 0.

–6 marks

1. Transform ds² = dx² + dy² + dz² into ds² = dr² + r² dq² +dz² and express it in terms

Christoffel symbol.

OR

1. i. State the Rigorous Quotient Law with an Illustration.
2. A quantity A (p,q) is such that A(p,q)B^q_s= C_ps where B^q_s is an arbitrary tensor and C_ps is a

tensor. Show that A(p,q) is a tensor. What is its type?

-14marks

4.a. Derive Einstein’s law of gravitation in empty space.

OR

1. b. Discuss about the principle of equivalence

 

–6marks

1. Derive the equation of Geodesic in the form

       

OR

 

2. d. Obtain the equation of the Geodesic for the metric ds² = -e^-2kt (dx² + dy² + dz² ) + dt².

–14marks

 

5.a. Prove that the Isotrophic polar coordinates in the form

OR

1. b. Discuss about Material energy tensor.

–6marks

 

 

1. c. Derive the deflection of light in passing through gravitational field in the neighborhood of the

sun.

OR

1. d. Derive the differential equation to the planetary orbits in the form

where   .

–14marks

 

 

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