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.
- a. i.what is Relativity?
ii..Explain the meaning of absolute quantities with examples.
iii..Is relativistic energy is absolute constant?
- Explain why Michelson-Morley experiment should be repeated during nights and days and
during all seasons of the year?
- What do you understand by Relativistic effects?
OR
- 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’.
- What is the rest mass of a light photon?
- What types of energies are included in E= mc2 ?
-6 marks
- c. Derive the Lorentz Transformations
OR
- d. i. Define Aberration and determine the relativistic value of Aberration and deduce its
classical value.
- Discuss about Doppler’s effect. –14marks
02 .a. Derive the transformation formula for force.
OR
- Derive the relativistic equations of motion and energy. -6 marks
- c. Discuss the concept of Minkowski space and Space-like and Time-like intervals.
OR
- 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
- If Bij = A i,j – A j,i, prove that B ij,k +B jk,i + B ki,j = 0.
–6 marks
- Transform ds2 = dx2 + dy2 + dz2 into ds2 = dr2 + r2 dq2 +dz2 and express it in terms
Christoffel symbol.
OR
- i. State the Rigorous Quotient Law with an Illustration.
- A quantity A (p,q) is such that A(p,q)Bqs= Cps where Bqs is an arbitrary tensor and Cps 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
- b. Discuss about the principle of equivalence
–6marks
- Derive the equation of Geodesic in the form
OR
- 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
- b. Discuss about Material energy tensor.
–6marks
- c. Derive the deflection of light in passing through gravitational field in the neighborhood of the
sun.
OR
- d. Derive the differential equation to the planetary orbits in the form
where .
–14marks