DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2017.
CLASSICAL AND STATISTICAL MECHANICS
(2008 Onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
20 100)
1. What are generalized co-ordinates? Obtain the
equation of motion of a system of two masses,
connected by an inextensible string passing over a
small smooth pulley (Atwood's machine).
What is Hamilton's principle? Arrive the Lagrange's
equations of motion from Hamilton's principle.
2. Write a note on generalized momentum and cyclic
co-ordinates.
State and prove principle of least action.
Obtain Hamilton's equations of motion.
3. Write the equations of motion in Poisson bracket
form and show that fundamental Poisson brackets
are invariance with respect to canonical
transformation.
Discuss about the Hamilton Jacobi theory in
detail.
Sub. Code
11
DE-649
2
Sp 6
4. Explain the canonical transformations and discuss
harmonic oscillator as an example of canonical
transformations.
Deduce the relations between the components of
linear and angular momentum using Poisson's
brackets.
5. Discuss the steady precession motion of a
symmetric top.
Summarize the applications of small oscillations.
Define moment of inertia.
6. Define Euler angles.
Derive Euler's equation of motion interms of Euler's
angles.
Obtain the normal frequency of a linear triatomic
molecule.
7. What is phase space?
State and prove Liouville's theorem.
Derive the energy fluctuations in canonical
ensemble.
8. Define partition function.
Discuss how thermodynamic functions are
calculated from it?
State and explain virial theorem.