Nalanda Open University
Annual Examination 2016
B.Sc. Physics (Honours), Part-III
Paper-V (Classical Mechanics and Mathematical Physics)
Time: 3.00 Hrs. Full Marks: 80
Answer any five questions. All questions carry equal marks.
1. Derive the equation of motion of a symmetric top. Discuss the special case
of a sleeping top.
2. What is Poison's bracket? State and prove its properties, Jacobin's identity
in particular.
3. Establish Hamilton Jacobi equation, and with its help solve the problem of
motion of a harmonic oscillator.
4. Prove that the sum of two tensore is also a tensor. Discuss the various
algebraic properties of tensors of arbitrary rank containing both covariant
and contravariant indices.
5. Using the method of separation of variables solve the differential
equation u Where u u t
dt
du
dx
du
2 .
What is Dirac delta function? Show that x
6. Discuss the solution of Laplace's equation. 0 2 in spherical polar co
ordinates
7. State and prove Canchy's Residue theorem.
8. State and prove Laurent's theorem.
9. Write the Lagrangian of motion of a double pendulum and deduce the
frequency of its motion.
10. Write notes on any Two of the following:
D'Alembert's principle
Gyroscopic Motion.
Hamitto's equation of Motion
Moment of inertia and products of inertia.