Bharathiar University 2001 M.Sc Physics Classical Mechanics,Statistical Mechanics and reality - Question Paper
Degree
22. (a) Explain how tharmodyaaiaic quantities cm be calculated in terms of partition, functions for grand canonical ensemble.
(b) Deduce Blcliaiisoa-Dtiskmaa equation of thermionic emission. Mention i s significance.
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(For the candidates admitted from 1999 aid m%mrd$)
M.Sc. DEGREE 1XAMMATION* APRIL 2001.
First Semester
Physics
Paper HI - CLASSICAL MECHANICS, STATISTICAL
Time: Three hours Maximum; 100 marks
SECTION A {10 x 2 = 20 marks)
Answer ALL questions.
Choose the correct answer.
1. Let L mi P represent the matrices of Lagrange ' and Poisson brackets respectively. Then,
|
(a) IP =3 |
 |
:f I
s
j I
2, Precession is rotation about
(a) j-axis (b) 2'-axis
space z-as (d) line of nodes,
3, Partition function is given, by
r r
t .Mr r
Cc) Electrons (i) Photons.
8. Relativistic Mastic energy is given by
(a) T2 =p2c2+m2e2 J,-ti T2 = p2c2 +m2e4
(c) T2 * /c2 + m4c2 (i) T2 = jA2 + mzc3.
! f t Answer the following questions in I- or 2 sentences : Uto-rawoS Oactoi#
, h 1 . . s t >6. Define Lagrange brackets, f w/y1 ) !?v$f .fc toaM.5
r 7- Tuat are Eulers angles?
" fwJv% /Sl 8. Statetheprope##fprtiioafunction.
p, ' .'X What ar|Boio|si Fermions?
, wt 3vy. 10, Explain the seine teiwor, ..v. .
SECTION B (5 x 4 = 20 marks)
Answer ALL questions, choosing either (a) or (b),
11. (a) Show that' Poissoa's bracket is invar under canonical transformation.
Or
Cb) Define action and angle variables,
12. (a) Explain moments and products of inertia,
. Ui
(b) What are normal co-ordinates and normal modes of vibration? .
13. (a) Explain, mean, root mean square and most probable velocities.
Or
(b) State and explain the law of equipartition of
.energy. ' '
14. (a) Compare M.B., B.E. and P.D. statistics.
Or
(b) Write a note on Bose-Einstein condensation.
15. (a) What is meant by Riemannian space?
. Or
v (b) Write a note on the rjelativistic generalisation of Newton's laws. . ,
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. SECTION" C (5 x 8 = 40 marks)
Answer ALL questions, choosing either (a) or (b),
16. (a) What is a c&adiikai transformation? Show that the transformation
ea cos p
t~a sin p is canonical.
Cb) Discuss Kepler's problem in aciiorv-angle
variables.
17. (a) Owe the th&ory of a symmetrical top moving under gravity.
Or
(b) (i) Give the theory of small oscillations,
(ii) Writs a note on the eigen value equation.
18. (a) (i) Explain partition functions and bring out their significance..
(ii) Writs a note oa M.B. distribution.
Cb) Discuss fully Doppler broadening of spectral
lines.
19. (a) Ci) Explain B.E. distribution*
(ii) Deduce Planck's law of Mack, body radiation,, applying B.E. distribution.
' Or
(b) Applying P.D. statistics, ' discuss Palis theory of Paramagnetism. .
20. (a) Discuss fully Lagraagiaa formulation of
relatmstie mechanics. .
Or
(b) Give brief accounts of
(i) Covariant Lagrangian fonattlation and
(ii) Covariant Hamiltonian formulation.
Answer ALL Questions, choosing either (a) or (b).
21. (a) Discuss fully the harmonic oscillator problem in Hamii ton-4acobi method.
Or
(b) Give the theory fef"detnaiamg the normal modes and normal frequencies of a linear matoiaic molecule. - -
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| Earning: Approval pending. |
