Note:
There are 10 questions with 2 questions from each unit. Students have to attempt 5 questions in all, selecting one
question from each unit. Each question is of 16 marks.
Unit - I
1.
(a) What are Cartesian and spherical polar coordinate systems? Find the
relation between the two. (10)
(b)
Derive expressions for area and volume element in cylindrical coordinates. (6)
2.
(a) What is Coriolis force? Derive an expression for
Coriolis force acting on a freely falling body. (10)
(b)
Explain inertial and non-inertial frames of references? (6)
Unit - II
3.
(a) Explain the laboratory and center of mass coordinate systems. Prove that
kinetic energies of two colliding particles in the centre of mass system are
inversely proportional to their masses. (12)
(b)
In laboratory system, two particles each of mass 2kg are moving with velocities
3i + 4j ms⁻¹ and 5i + 6j ms⁻¹
respectively. Find the K.E. of the system of two particles in COM system. (4)
4.
(a) Show that for a system of two particles moving under the action of central
force, the total energy of the system remains conserved. (10)
(b)
Establish relation between eccentricity and energy. (6)
Unit - III
5.
(a) What is Helmholtz resonator? Derive an expression for its frequency. (10)
(b)
Calculate the frequency of an L-C circuit in which the inductance and
capacitance are respectively 5 mH and 2 μF. If the maximum potential difference
across the capacitor be 10 volts. What is the energy of the system? (6)
6.
(a) What is a quality factor? Discuss quality factor in a damped harmonic
oscillator. (6)
(b)
Derive an expression for energy of a damped oscillator. (10)
Unit - IV
7.
(a) Define a forced oscillator: Write down the equation of a driven harmonic
oscillator and solve the equation which gives the steady state behaviour of the
forced oscillator. (10)
(b)
Derive an expression for the velocity of the forced oscillator in steady state. (6)
8.
(a) Derive an expression for average power in a forced oscillator and discuss
the result. (10)
(b)
Obtain an expression for band - width. (6)
Unit - V
9.
State fundamental postulates of special theory of relativity and deduce from
them the Lorentz transformation equations. (16)
10.
(a) Discuss relativistic variation of mass with velocity. Show that no material
body can move with velocity greater than that of light in vacuum. (10)
(b) In Michelson - Morley experiment, the wavelength of the
monochromatic light used is 5000 Å. What will be the expected fringe shift on
the basis of stationary ether hypothesis if the effective length of each path
be 5 metres? Given velocity of the earth is 3 × 10⁴
m/s. (6)
