M.Sc. DEGREE EXAMINATION, APRIL 2016
Physics
CLASSICAL MECHANICS
(2011 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 2 20)
Answer all questions.
1. State the D'Alembert's principle.
2. What are Ignorable coordinates?
3. Show that the transformation Q p P qp2 is
canonical.
4. State the Hamilton-Jacobi theory.
5. Give the theorems about the moment of inertia.
6. Write Euler's equations of motion for a rotating rigid
body.
7. What do you mean by relativity? State the two postulates
of relativity.
8. Rest mass of an electron is 9.1 10-31 kg. Calculate its
mass when it is moving with a velocity 0.8 c.
9. What is single stage and multi stage Rocket?
10. Define specific impulse.
Sub. Code
521101
RW-10942
2
Wk 11
Part B 5 25)
Answer all questions choosing either or
11. State and prove the principle of virtual work.
Or
A particle of mass m attached to a spring of force
constant k is executing a SHM about the
equilibrium position. At an instant the
displacement of the particle from the equilibrium
position is x and its velocity is v. Write down
Lagrangian of the system and find the equation of
motion.
12. Discuss about the Hamilton-Jacobi theory.
Or
Show that the transformation
2
P 1 p2 q2
p
Q q is canonical.
13. Explain the principle axes inertia.
Or
Derive an expression for Kinetic energy of a rigid
body.
14. Discuss the length contraction under Lorentz
transformation.
Or
Calculate the velocity at which the mass of a
particle becomes double of its rest-mass.
RW-10942
3
Wk 11
15. Write any two exhaust speed parameters.
Or
Derive an equation for the thrust of a rocket.
Part C 10 30)
Answer any three questions.
16. Derive the Lagrangian equation of motion under
conservative force field. Construct Lagrangian equation
of motion for a simple pendulum.
17. State and prove principle of least action.
18. Derive the angular velocity and kinetic energy of a
rotating body in terms of Euler angle.
19. Discuss in detail the Lorentz transformations
20. Describe in detail the optimization of a multi-stage
rocket.