University Of Pune Model Question Paper MSc Physics : www.unipune.ac.in

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Document Described : University Of Pune - Model Question Paperz
[4024] - 101
M.Sc. (Sem. - I)
PHYSICS
PHY UTN - 501 : Classical Mechanics
(2008 Pattern) (New Course)
Time : 3 Hours] [Max. Marks : 80

Model Question List : http://www.unipune.ac.in/university_.../paperSci1.htm
Model Question Paper : http://www.unipune.ac.in/university_...cs_oct2011.pdf

Instructions to the candidates:
1) Question No. 1 is compulsory and solve any Four questions from the remaining.
2) Draw neat diagrams wherever necessary.
3) Figures to the right indicate full marks.
4) Use of logarithmic table and electronic pocket calculator is allowed.

Q1) Attempt any four of the following :
a) Apply the principle of virtual work to obtain lever equation. [4]
b) Show that the constraints acting in the case of a rigid body are conservative. [4]
c) A bead slides on a smooth rod which is rotating about one end in a vertical plane with uniform angular velocity W. Show that the equation of motion is m r  = mrw2 – mg sin(wt). [4]
d) Describe the Hamiltonian and Hamilton’s equations for an ideal spring mass arrangement. [4]
e) Show that the transformation Q = P 1 , P = 9P2 is canonical. [4]
f) Use Hamilton’s equation to prove that the areal velocity is constant in planetary motion. [4]

Q2) a) A disc of radius ‘a’ and mass ‘m’ rolls down an inclined plane making an angle ? with the horizontal. Set up the Lagrangian and find the equation of motion and acceleration of the disc. [8]
b) Prove viral theorem. [4]
c) Deduce Hamiltonian for a compound pendulum and Hamiltons equations of motion. Also calculate the period of its oscillation. [4]

Q3) a) Obtain an expression for coriolis acceleration for rotating co-ordinate system. [8]
b) Derive Hamiltonian function and Hamilton’s canonical equations of motion. What is the physical significance of Hamiltonian function. [8]

Q4) a) Derive Euler-Lagrange equation and using variational principle show that geodesics of a spherical surface are great circles. [8]
b) Deduce Hamilton’s principle and use it to find the equation of one dimensional harmonic oscillator. [4]
c) Write note on artificial satellite. [4]