M.Sc. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2017.
First Semester
Physics
CLASSICAL MECHANICS
2 20711-A
Time 3 Hours Max. Marks 70
PART — A
(Short answer type)
Answer any FIVE questions.
All questions carry equal marks. x 6 30 Marks)
1. Prove that the shortest distance between two points in a plane is extreme.
2. Find the solution for Atwood's machine using Lagrange's equations of motion.
3. Define cyclic co-ordinates and mention their advantages.
4. Prove that the Rayleigh's dissipation function is equal to one half of the rate of
work done against friction.
5. Define Legendre transformations and apply it to thermodynamics.
6. Show that the Poisson bracket is invariant under canonical transformations.
7. Write notes on action angle variables.
8. Define normal modes and normal co-ordinates. Obtain normal modes for water
molecule.
PART — B
(Essay type)
Answer ALL questions.
All questions carry equal marks. x 10 40 Marks)
9. Define D'Alembert's principle and obtain Lagrange's equations from it for
conservative systems.
Or
State and prove energy conservation theorem for a system of particles.

10. Extend Hamilton's principle to non-conservative and non-holonomic systems.
Or
Obtain Hamiltonian-Jacobi equation and find the solution for linear harmonic
oscillator using this method.
11. Define Canonical transformations and obtain transformation equations for
F1 and F4 generating functions.
Or
What are the differences between and variations? Obtain the relation
between them and also state and prove principle of least action.
12. Obtain the Eigen value equation and apply group theory to normal modes of
vibration.
Or
What do you mean by reducible and irreducible representations? Obtain the
character table for C2v and C3v groups.
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