M.SC PHYSICS CLASSICAL MECHANICS QUESTION PAPERS

I Semester M. Sc Degree Examination
PHYSICS: Classical Mechanics
Time: 3 Hours Max. Marks: 80
1. a) Prove that the sum of PE and KE remains constant for a system of particles
moving under the action of a conservative force.
b) Define centre of mass for a system of particles (10+5)
(OR)
2. a) Starting from D’Alembert’s principle, derive an expression for Lagrange’s
equations of motion.
b) What are constraints? Write their classification. (10+5)
3. a) Derive Hamilton’s canonical equations of motion from variational principle.
b) Obtain Hamiltonian for one dimensional simple harmonic oscillator. (10+5)
(OR)
4. a) Define the term ‘canonical transformation’ and hence derive the condition for a
canonical transformation.
b) Define Poisson bracket and express Hamilton’s equation of motion using Poisson’s
equation. (10+5)
5. a) Using Hamilton –Jacobi method solve one dimensional harmonic oscillator
problem.
b) State and prove parallel axis theorem. (10+5)
(OR)
6. a) Set up Euler equations of motion for a rigid body.
b) What do you mean by inertia? Explain its physical significance. (10+5)
7. a) Deduce
2 2 2 2 4 E p c m c   o
b) Discuss the simultaneity in relativity. (10+5)
(OR)
8. a) Deduce Newton’s gravitational theory from Einstein’s field equations.
b) What is meant by principle of covariance? Differentiate between covariance and
invariance. (10+5)
9. Answer any FOUR of the following. (5 x 4=20)
a) Check whether force
2 2 ˆ ˆ
F x xy i y x j     (2 5 ) (3 4 )

is conservative or not.
b) Obtain the equation of motion for Atwood machine.
c) Give the significance of Hamiltonian function.
d) Using Poisson brackets show that the following transformation is canonical:
2 cos 2 sin t t Q qe p and P qe p  
e) Show that the kinetic energy of a rotating rigid body can be written as
1
2
T J  
f) Calculate the inertia tensor for the system of four point masses 2g, 3g, 4g and 6g
located at the points (1,0,0), (1,-1,0), (1,1,-1) and (1,-1,1).
g) At what speed does a meter stick move if its length is observed to shrink to 0.5m?
h) Describe the equivalence principle.