Write Hamilton-Jacobi equation and explain its importance.

Obtain the expressions for normal frequencies and normal modes of a symmetric linear triatomic molecule.

What is length contraction? Derive an expression for the contracted length.

Write Minkowski space-time diagram and explain classification of events based on it.

With neat diagrams explain how Euler angles are defined.

Discuss the motion of heavy symmetric top rotating under the action of gravity with one point fixed.

Explain the evidences of mass-energy equivalence and describe Eotvos experiment.

Three particles of masses 2kg, 2.5kg and 3.5kg are placed at points (2,0,2), (0.3.2) and (-2,-2,0) respectively. Determine the coordinates of the center of mass.

A body of mass m is thrown as a projectile. Construct the Lagrangian and determine the equations of motion.

The orbit of a particle of mass moving in a central force is given by r= k0², where k is a constant. Show that the following transformation is canonical.