MATHEMATICS Guessing paper

Guessing paper

B.Sc – Final

MATHEMATICS

(optional )

Paper-3 (Special Theory of relativity)

1. (A) Obtain general and simple Galilean transformation.

(B) Show that Lorentz-Fitzgerald contraction hypothesis Implies that there is no fringe shift.

OR

(C) State the two postulates of special relativity Theory.
(D) Obtain the Lorentz transformation equeation.

2.

(A) discuss time dilation in special relativity.
(B) Show that in nature no signal ca move with a Velocity greater than the velocity of light relative to Any inertial system.
OR
(C) Obtain the transformation of particle velocities.
(D) Deduce the Einstein’s velocity addition low from The transformation of particle velocities.
3.

(A) Deduce the transformations for an antisymmetric For tensor Trs.
(B) Prove that two events which are separated by a Time like interval cannot occur simultaneously in Any inertial system.
OR
(C) Define:
(1) Contra variant vector.
(2) Covariant vector.
(3) Time like Interval.
(4) Space like interval.
(5) Light like interval.

(D) Define four tensor Trs and write sixteen Components of Trs in matrix form.

4.

(A) Obtain the mass energy equivalence E=mc2.
(B) Define four velocity and prove that the four velocity Of a particle is a unit time like vector.
OR
(C) Obtain equation of motion for a free particle.
(D) Obtain expression for relativelistic Lagrangion L.
5.

(A) Write he Maxwell’s equation of electromagnetic Theory in vacuum in component form.
(B) Obtain a wave equation for the propagation of The electric field strength E in free space with Velocity C.
OR
(C) Obtain transformations for electric field strength.
(D) Prove that the energy momentum tensor of Electromagnetic field is trace free.