Bharathidasan University
S.No. 6604
(For candidates admitted from 2008-2015 onwards)
M.Sc., DEGREE EXAMINATION, APRIL 2021.
Physics
CLASSICAL DYNAMICS AND RELATIVITY
Time : Three hours Maximum : 75 marks
PART A — (10 x 2 = 20)
Answer ALL questions.
1. What are internal and external forces?
2. State D’Alembert’s principle.
3. Define moment of inertia and product of inertia.
4. Write down the expressions for Eulers equation of motion for a rigid body.
5. Define Poisson bracket of any two dynamical variables.
6. Give the condition for canonical transformation.
7. What do you understand by Chaos?
8. Differentiate free and damped oscillations.
9. Differentiate stable and unstable equilibrium.
10. What are four vectors?
PART B — ( 5 5 = 25 )
Anser ALL questions, choosing either (a) or (b)
11. (a) State Hamilton’s principle and explain Hamilton’s principle function.
Or
(b) Write short notes on symmetry properties of space and time.
S.No. 6604 2
12. (a) Discuss the problem of symmetric top under the action of gravity.
Or
(b) Write about normal coordinates and normal modes of vibrations.
13. (a) State and explain the principle of least action.
Or
(b) Derive Hamilton’s Canonical equations of motion.
14. (a) Bring out one soliton solution
Or
(b) Distinguish between linear and non-linear systems.
15. (a) What are the basic fundamentals of special theory of relativity?
Or
(b) Discuss about Minkowski space and Lorentz transformation.
PART C — ( 3 10 = 30 )
Answer any THREE questions
16. Describe the scattering in a central force field.
17. Discuss the small oscillations of the CO2 molecule and obtain the frequencies of their modes.
18. Solve Kepler’s problem using action - angle variables.
19. Write a detailed note on
(a) Solitary waves (5)
(b) applications of solitons (5)
20. Describe velocity four vector, momentum four vector,
acceleration four vector and minkowski’s force as examples of four vector.
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