M.Sc. DEGREE EXAMINATION, NOVEMBER 2017
First Semester
Physics
CLASSICAL DYNAMICS AND RELATIVITY
(CBCS 2014 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 x 2 20)
Answer all questions.
1. Deduce Newton's second law of motion from Hamilton's
principle.
2. Define a cyclic co-ordinate.
3. Write examples for central force.
4. For a particle under central force explain conservation of
energy.
5. Write down expressions for rotational kinetic energy and
moment of inertia of a rigid body.
6. Explain 'precession' and 'nutation' motion for a spinning
top.
7. What is Fermat's principle.
Sub. Code
4MPH1C2
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8. Define action variables and angle variables.
9. Define a transformation and a point transformation.
10. What is the force acting on a particle with charge q .
Write its expression.
Part B x 5 25)
Answer all questions, choosing either or
11. For a system of particles, using Newtonian
mechanics explain the conservation theorem for
angular momentum.
Or
Arrive at Lagrange's equation of motion for a
spherical pendulum.
12. For central force 2
r
f r R using Hamilton's
equations find the equations of planetary motion
and prove areal velocity is constant.
Or
A particle of mass moves under the influence of
central force with potential V Rmr3
state the condition for circular motion to take place,
find its period of revolution.
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13. Derive Euler's equations for the motion of a rigid
body with one point fixed.
Or
Explain the processional motion of a top without
nutation and with nutational motion.
14. Prove that Lagrange's bracket is invariant under
canonical transformation.
Or
State and prove the principle of least action.
15. Explain Lorentz Fitzgerald contraction and time
dilation.
Or
Derive Mass energy equivalence energy relation.
Part C 10 30)
Answer any three questions.
16. Derive Lagrange's equations of motion from Hamilton's
variational principle for a conservation system and
for a non-conservative system.
17. Explain the general features of orbits under the inverse
square law of force for various value s of k
18. Explain angular velocity and angular momentum of a
rigid body. Write a brief note on moments and products of
inertia.
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19. Solve Harmonic oscillator problems using action
angle variable method.
Obtain the equations of motion in Poisson bracket's
form.
20. Explain four velocity, four force, four momentum. Obtain
expressions for relativistic kinetic energy and Relativistic
mass.
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