problem 1:

a) State the D’Alembert’s principle and obtain the Lagrange’s equation from it.

b) State and describe principle of least action.

problem 2:

a) What do you understand by the independent coordinates of a rigid body?

b) Describe the coriots force and its importance.

problem 3:

a) State and describe the basic postulator of spatial theory of relativity and get Lorentz transformations.

b) Describe conanical transformation with illustrations.

problem 4:

a) What do you mean by action angle variable? Describe the use of such variables to the problems of Kepler’s laws.

b) Formulate the theory of small oscillations.

problem 5:

a) State and describe equi-partition theorem.

b) What do you mean by Gibb’s paradox? Describe how it has been resolved.

problem 6:

a) Describe the energy fluctuations in the canonical ensemble.

b) Obtain the equivalence between the canonical ensemble and grand canonical ensemble.

problem 7:

a) Describe the postulate of quantum statistical mechanics.

b) Describe the Darwin–Fowler method for finding out the partition function.

problem 8:

a) Obtain an expression for the internal energy of an ideal Fermi gas.
b) Describe Bose-Einstein condensation.

problem 9: prepare notes on any two of the given:

a) Hamilton’s principle.
b) Canonical invariance.
c) Density punctuations in the grand canonical ensemble.
d) Theory of white-dwarf.