Note
– There shall be 10 questions with 2 questions from each Unit. Students have to select one question
from each Unit. Total no. of
questions candidates have to attempt is 5.
Unit I
1. (a) Find velocity and
acceleration of a particle in case of spherical polar coordinates. (12)
(b) The
motion of a particle is given by x = 5t - 9, y = 2 cos 3t, z = 2 sin 3t. Find
the magnitude of velocity and acceleration of the particle. (4)
2. (a) Derive expressions for unit
vectors in cylindrical coordinate and prove that they are mutually
perpendicular to each other. (10)
(b)
Discuss Geographical effects of Coriolis force. (6)
Unit II
3. (a) Prove that in COM system, the
magnitude of the velocities of the particles do not change in elastic
collisions. (10)
(b)
Prove that angular momentum of reduced mass under the effect of the central
force is conserved. (6)
4. (a) Define central and
non-central forces. Derive the differential equation of the orbit. (10)
(b)
State Kepler’s laws of planetary motion and derive Kepler’s third law. (6)
Unit III
5. (a) Derive expressions for
differential equation and time period in case of Bifilar pendulum. (10)
(b)
Calculate the energy possessed by a stone of mass 20 gm executing S.H.M of
amplitude 1 cm and time period 4 seconds. (6)
6. Define the following terms in
case of damped harmonic oscillator: (10)
(i) Relaxation time
(ii) Logarithmic decrement
and derive expressions for them.
Unit IV
7. What is a driven oscillator?
Discuss transient and steady-state behaviour of forced oscillator. (16)
8. (a) Show that average power
supplied by the driving force to the oscillator is equal to the average power
dissipated against frictional force. (10)
(b) Find
the resonant frequency of a ckt. having L = 1 mH, C = 0.1 μF and R = 10 Ω.
Also, calculate bandwidth and quality factor of the ckt. (6)
Unit V
9. Derive Lorentz transformation
equations for two inertial frames and apply these to explain length
contraction. (16)
10. (a) Deduce the mass-energy
relation E = mc². Give significance of this relation. (10)
(b) An
electron is accelerated through a potential difference of 1.8 × 10⁶ V. Find the relativistic mass of the electron.
Given m₀ = 9 × 10⁻³¹ kg. (6)
