Bharathiar University 2003 M.Sc Physics Classical Mechanics,Statistical Mechanics and reality - Question Paper

Degree

Match the following:    SECTION B - (5x6 = 30 marks)

11, Canonical transformation (a) Maxwel-Boltanaaa distribution law ' 12.    Nutation 13,    Molecules of a gas 14,    Neutrons 15.    Four dimensional (c) Symmetric top {.2U- \{dj    iiivemwii (e) Fermi-Dirac distribution law Answer in 1 or 2 sentences : IS, What are canonical transformations? . O' 9>"V a ,, What is a sleepig top?_ 18. Define partition fonction P 19. Write down . Richardson-Dushman equation of thermionic emission. I J 20- Write down Dopplers relavistic formula for light .waves in vacuum.

Answer ALL questions, choosing either (a) cr (b)X \ 21,    (a) Prove any two properties of poisson bracket.' Or (b) Find the solution to harmonic oscillator problem by Hamilton-Jacobi method. 22 ,.....(a) Explain briefly Bulers angles. Or (b) Explain the terms normal coordinates and normal modes of vibration, 23,    (a) Obtain expressions for most probable speed, mean speed and root mean square speed from Maxwell-Boltzmann distribution law. Or (b) State and explain the principle of eqnipartition of energy.

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24,    (a) Discuss briefly the phenomenon of Bose-Einstein condensation.

Or

(b) Compare M.B., B,E, and F.D. Statistics,

25.    , (a) Obtain Einstein's relation between momentum and metgy.

Or

(b) Write a note on relativistic generalization of Newton's laws..

SECTION C (5 x 10 = 50 marks)

Answer ALL questions, choosing either (a) cr (b).

,28. (a) For what .values of m and n do the "transformation equations

Q-q^m cosn p

P = q^m sin tip '

Present a canonical transformation?

Or

(b) Solve Kepler's problem ' by Action-Angle

variable,

27.    (a) Discuss the motion of a symmetrical top with one point fixed. Explain dearly what are nutational and precessional motion.

Or

(b) Illustrate the technique of norma! coordinates analysis with a linear triatomic molecule.

28.    (a) State Maxwell-Boltzmann distribution lav/. Establish Maxwell's law of distribution of velocities.

Or

(b) Obtain the relations connecting the partition function and the various thermodynamical quantities such    E, Helmhclte free energy F, entropy 8

and specific heat

29.    (a) State Bose-Einstein distribution law. Deduce Planck's law from Bose-Einstein law.

Or

(b) Deduce Richardson-Dushmann equation of thermionic emission. . .

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4S03    [02 23 68]

(For the candidates admitted from 2002 and onwards) M.Sc. DEGREE EXAMINATION, APRIL 2003, first Semester Physics

Paper II CLASSICAL MECHANICS, STATISTICAL MECHANICS AND RBLATOTT?

Time; Three hoxqs    Maximum: 100 marks

SECTION A(20x1 20 marks)

Answer ALL questions.

Choose the correct answer:

1, If I, and P denote the- matrices of Lagrange and

Poisson brackets respeetiyely, then

When the moment of inertia tensor I operates on angular velocity vector W, :he resulting angular momentum vector L is- given by

l*iw    m i=i²f

1    '    w

(c) L as =    {d} Ii =* W    I

S. The Maxwell~Bolt2mann distribution law is applicable to

(a) identical and iadistinguishable particles

identical and distinguishable particles

(c)    unidentical and disusguishable particles

. (d) umdeatkai and indistinguishable particles.

is

\

4, Buse-Einstein condensation is described as a

V"

(a).    condensation is phase space

(b)    condensation in Hben space

(c) condensation in eonfiriitiion spm?

(d)    condensation is znomentim space.

4203

5. The relativistie relation for the variation of mass with velocity is

(a) m = "jamjSat

1_{1 +} v*tn*

#+FVC*

Fill up the blanks:

6,    Poisson brackets are *2&&Hvith respect to canonical transformations,

7,    The configuration oLrf rigid body would be

completely specified by;^,-vj?^r~- degrees of freedom,

8,    According to the principle of eqxdpartition of energy, the av rige energy associated with each degree of freedom is rI

9,    The minimum amount of energy necessary to remove an electron, from the metal is known as ~fcSv^:

10,    The time is no mom a scalar invariant and changes raider------ ,

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30. (a) Explain briefly Lore'ntz transformation of electric and magnetic field components.

Or

(b) Give a brief account of the Hamiltonian formulation of the relatMstic mechanics.

Attachment: bharathiar-university-2003-m-sc-physics-19846-1.pdf bharathiar-university-2003-m-sc-physics-19846-2.pdf bharathiar-university-2003-m-sc-physics-19846-3.pdf bharathiar-university-2003-m-sc-physics-19846-4.pdf bharathiar-university-2003-m-sc-physics-19846-5.pdf

Earning:   Approval pending.