Bharathiar University 2004 M.Sc Physics Classical Mechanics,Statistical Mechanics and reality - Question Paper
Degree
Reg, No.
09 23 58]3155
(For the candidates admitted from 1999-2001) M.Sc. DEGREE EXAMINATION, APRIL 2004.
First Semester Physics
CLASSICAL MECHANICS, STATISTICAL
MECHANICS AND RELATIVITY
Time; Three hours Maximum; 100 marks
'SECTION A (10x2 = 20 marks)
' Answer ALL questions.
Choose the correct answer:
1. The frequency of the harmonic jcittator is
I
2. The minimura spin angular velocity below which
the top cannot spin stably about vertical axis when
1 . . ' a * , is given by
2
Ca)
 |
|
2 mell li/a |
I. 11 S 1
imgl 1;
*
a.
-8 i I :.| ;
i/
3, Most probable speed is
IF
Ca) C ;
(b)
5
t
[2m jIkT
! m
nr
(cl) '1.59",
m
I!
3 ;
:
U
4. Richardsoa -Dushman equation of thermionic
-emission is
(a) J sATte,vikT Qp/j *AT*e~?*ik7 Cc} J=ATem (d) J = ATe~**/ir.
a
*
i<
\
5. According to Hamiltonian formulation relativistic mechanics
\
|
(a) |
H |
~T ~mC2 |
~q$ |
|
(b) |
H |
= T+mC* | |
|
(e) |
H |
ii *3 i 3 o ft* |
+ # |
|
(d) |
H |
=f+wC2 |
+#. |
|
Answer : |
in 1 or 2 sentences : | ||
8. ' What is Hamilton's principal fonction? __ .
s & - u ifk. otntwCm -gurc-
7. What are Euler's angles? *W>o2i W
to 0
8. State the law of equipartffian of
9. What are Fermonso IfcJw
1 imdsi cmima *h ml
10. What is metric tensor? (% ar
Jc-c aMociciiii vvilt, agutln dU SECTIONB -*- (5 x 4 = 20marks) y. tT.
,!/
Answer ALL questions, choosing either (a) or (b), %o%
11. (a) Whet are canonical transformations? Give zn
example,
, ... -Or
(b) Define Lagrange and Boisson brackets.
3 ' 3155
>
20. (a) Explain relativistic generalization of
Newtons laws,
....... Or
(b) Explain Hamiltonian formulation of relativistic mechanics.
SECTION D (2 x 10 = 20 marks) _
Answer ALL questions, choosing either (a) or (b),
21. (a) Deduce Hamilton-Jacobi partial differential equation. Discuss harmonic oscillator problem by Hamilton - Jacobi method.
Or
(b) Discuss he motion of a symmetrical top with one point fixed.
v - .
22. (a) Obtain the relations connecting the partition function and the various thermodynamical quantities such as energy E, Helmholtz free energy f entropy S
and specific beat.
' ' Or"- ' '
w . tie and explain Fermi-Dirac distribution law. Discuss Pauli's theory of paramagnetism.
12, (a) Explain moments and products of inertia.
(b) What are normal modes and mrmm coordinates ofvtbrution9
18. (a) State and explain MaxweKBefczmann distribution law.
(b) Wrke a note on Doppler broadening of spectral lines. - '
14. fa) Applying B.E. statistics, derive Planck's radiation formula.
Or
*
(b) Compare M.B., B.E. and F.Dr statistics.
15. (a) Write a note on the Riemann tensor.
(b) State and sxpkln Loret? frmsh'apnn equations. 1
SECTION C - (5 x 8 * 40 marks)
Answer ALL questions, choosing either (a) or (b),
18, (a) Derive the equations of motion in Poisson brackets notation.
Or
(b) What are actios and angle variables? Explain briefly any one of Its applications,
17, (a) Derive Eulers equations of motion.
Or
(b) Discuss the free vibrations of a linear triatomic molecule,
18, (a) Applying the law of eqmpartition of energy, obtain an expression for fee mean energy of harmonic oscillator.
' Or
(b) Derive expressions for the most probable, average and root mean square speeds.
19, la) Discuss briefly Bose-Einstein condensation.
Or
(b). Derive Richardsoa-Dushman equation of thermionic emission.
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Attachment: |
| Earning: Approval pending. |
