25.

26.

28.
29.

30.
31.

89.
88.
34.
35.

3 D 91716

Section D

Answer any four questions.
Each question carries 4 marks.

If F= (2xy + 2 1 + ಜೈ + ‏پر د2‎ newton, then show that it is conservative. Calculate the amount of
work done by this force in moving a particle from (0, 1, 2) to (5, 2, 7) m.

A clock keeps correct time. With what speed should it be moved relative to an observer so that it
may seem to lose 2 minutes in 24 hours ?

Obtain the equation of motion of a simple pendulum by using Lagrangian method and hence
deduce the formula for its time period for small amplitude oscillations

Calculate the speed of an electron which has kinetic energy 2 MeV.

The eccentricity of the earth’s orbit is 0.0167. Calculate the ratio of maximum and minimum speeds

of the earth in its orbit.
Write the Hamiltonian for a simple pendulum and deduce its equations of motion.

Determine the Iength and the orientation of a rod of length 10 metres in a frame of reference
which is moving with 0.6c velocity in a direction making 30° angle with the rod.

(4 x 4 = 16 marks)
Section E

Answer any two questions.
Each question carries 10 marks.

Explain and deduce Hamilton’s equations.

Briefly explain and deduce Inverse square law of planetary motion.

Explain conservation theorems and symmetry laws.

Explain Galilean transformation and deduce Galilean transformation equations.

(2 x 10 = 20 marks)