DISTANCE EDUCATION
M.Sc. DEGREE EXAMINATION, MAY 2016.
Physics
CLASSICAL AND STATISTICAL MECHANICS
(2008 onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
20 100)
1. Explain Hamilton's variational principle.
Derive Lagrange's equation from D'Alembert's
principle.
Explain the principle of virtual work.
2. State and explain the principle of least action.
Derive Hamilton's equation of motion from
variational principle.
Show that Poisson bracket is invariant under
canonical transformation.
3. Discuss Hamilton Jacobi's theory in detail.
Derive equation of motion under canonical
transformation.
Sub. Code
11
DE-3831
2
wk9
4. Show that the transformation
P
Q 1 and P qp2 .
is a canonical transformation equation.
Derive the equation of motion interms of Poisson
bracket.
Calculate kinetic energy of a rigid body.
5. Explain Principle axes of inertia in a rigid body.
Explain Euler's angle in detail.
6. Describe conservative and non-conservative
systems.
Explain the small oscillations of CO2 molecule.
What do you mean by cyclic co-ordinates?
7. Apply Maxwell Boltzmann statistics and obtain
expression for velocity distribution.
Deduce expressions for r.m.s. and most probable
velocities.
What is meant by partition function? Explain its
importance in statistical mechanics.
8. What is Helmholtz function? Show that it
represents the free energy of the system in
reversible isothermal process or the energy
available for work?
Write notes on Canonical and grand Canonical
ensemble.
Write down the properties of ideal Fermi gas.