Calicut University 2007-1st Sem M.Sc Physics Phy 103 – CLASSICAL MECHANICS- -UARY - Question Paper

1st SEMESTER M.Sc. DEGREE EXAMINATION, JANUARY 2007
Physics
Phy 103 – CLASSICAL MECHANICS
(2003 admission onwards)

Time: 3 Hours Maximum : 80 Marks

part A

ans any 5 ques..
every ques. carries four marks.

1. State and discuss De Alembert’s principle.

2. Show that the generalized momentum conjugate to a cyclic co-ordinate is conserved.

3. Show that the Hamiltonian of a system can be found from its Lagrangian through a transformation.

4. How does the Hamilton-Jacobi formula help in the transition of Classical Mechanics to Quantum Mechanics?

5. State the sequence of transformations in the definition of Euler angles.

6. With a suitable example, illustrate the Corioli’s force.

7. Outline the idea of normal modes in coupled systems.
(5 x four =20 marks)

part B

ans any 2 ques..
every ques. carries 20 marks.

8. (a) Derive the Euler-Lagrange formula. Apply it to the compound pendulum to find the period of oscillation.

Or

(b) Solve the Kepler’s issue by Hamilton-Jacobi method and explain the outcomes.

9. (a) Derive the formula of motion of a rigid body. Using it, explain the torque free motion of a rigid body and bring out the idea of the inertia ellipsoid.

Or

(b) Set up the Eigen value formula for the issue of small oscillations. Solve it, highlighting the principal axis transformation.

(2 x 20 = 40 marks)

part C

ans any 2 ques..
every ques. carries 10 marks.

10. A particle of mass m is projected with an initial velocity u at an angle a to the horizontal. find the Lagrangian of the system and hence show that its position is defined by


11. A particle of mass m is constrained to move on the surface of a cylinder. The particle is subjected to a force directed towards the origin and proportional to its distance from the origin. find the Hamilton’s formula of motion of the system and show that the motion of the particle in z- direction is simple harmonic.

12. Solve the issue of the linear harmonic oscillator using action-angle variables.

13. A particle of mass m is free to move along a straight line and is attached to a spring whose other end is fixed at a point A, at a distance of l from the line. A force F is needed to extend the spring of the length l. find the frequency of small oscillations of the mass.

(2 x 10 = 20 marks)

Earning:   Approval pending.