DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2018.
CLASSICAL AND STATISTICAL MECHANICS
(2008 onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
x 20 100)
1. Obtain Lagrange's equations of motion.
Obtain the Lagrange's equation of a simple
pendulum.
State and explain D'Alembert's principle.
2. State and explain Hamilton's variational principle.

Write a note on conservative and non-conservative
systems.
What are generalized coordinates? Explain.
3. State that Poisson's brackets are invariant under
canonical transformations.
Deduce Hamiltonian equations of motion.
What do you mean by action and angle variables?
Explain.
Sub. Code
11
DE-4057
2
wk10
4. State and prove the principle of least action.
Discuss the elements of Hamilton-Jacobi theory.
What are canonical transformations? Explain.
5. Deduce Hamilton-Jacobi equations and discuss its
physical significance.
List the Poisson's bracket relations.
Write a note on infinitesimal canonical
transformation.
6. Give the theory of small oscillations.
What are Euler angles? Bring out their meaning.
Discuss motion of symmetric top under the action of
gravity.
7. Deduce Maxwell's distribution of velocities, mean,
root mean square and most probable velocities.
State and prove Liouville's theorem.
Write a note on canonical ensembles.
8. Write a detailed note on microcanonical ensemble
theory and its application to ideal gas of
monoatomic particles.
Discuss grand canonical ensembles theory.
Deduce the viral theorem.
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