Madurai Kamraj University (MKU) 2006 M.Sc Physics - Question Paper

CLASSICAL MECHANICS AND STATISTICAL MECHANICS


Time: 3 Hours Maximum:100 Marks

ans all ques..
(5×20=100)

1.(a) (i) State D'Alembert’s principle deduce largrange’s equations of motion from D' Alembert’s Principle.

(ii) Apply lagrange’s equations to slove:

1)The Atwood’s machine and
2)Simple Pendulum.

OR

(b) (i) State and discuss Hamiltion’s principle.deduce lagrange’s
equations from Hamilton’s from Hamiltons principle.

(ii) find the velocity of a loop rooling down an inclined plane.

2.(a) (i) How do you convert a 2 body issue into 1 body problem? find expressions for position and time through formula of motion and 1st integral.

(ii) State and prove virial theorem.

OR

(b) (i) Write the Euler’s theorem on the motion of rigid body. discuss the idea of infinitesimal rotation.

(ii) elaborate Euler’s angles? discuss the various rotations of it.

3.(a) (i) discuss the theory of small oscillations. Apply it to solve the linear molecule issue.

(ii) Write an account on normal co-ordinates.

OR
(b) (i) State and prove the principle of lowest action.

(ii) Derive the Hamilton’s equations from variational principle.

4.(a) (i) Derive the canonical transformation equations.

(ii) discuss the canonical invariance of lagrange bracket.

OR
(b) elaborate action- angle variables? Solve the Kepler issue based on action- angle variables.

5.(a) explain the kinds of statistics in detail.Derive the Sackur-tetrode formula for a mono atomic ideal gas.

OR

(b) discuss in detail the Brownian motion.

Earning:   Approval pending.