M.Sc First Semester Physics (Classical Mechanics) Question Paper 2024 Pdf

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Roll No……..

B010702T
M.Sc. (First Semester)
(NEP) EXAMINATION, 2023-24
PHYSICS
(Classical Mechanics)

Time : 2 Hours ]                                                                                                                   [ Maximum Marks 75

Note : attempt questions from all sections as directed.

Instruction : The candidates are required to answer only in serial order if there are many parts of equation answer them in continuation.

Section – A
(Short Answer Type Questions)

Note : All questions are compulsory each questions carries 5 marks

1 (A) Write down the principle of least action

(B) Define constraints

(C ) What do you mean by cyclic coordinates.

(D) Explain variational principal in brief
(E) Briefly describe the principle of virtual work
(F) State Noether’ theorem.

(G) For a Harmonic Oscillator T = ½ mx² and U = ½ kx² 4 and equilibrium position xo = 0, find out Langrange equation of motion.

Explain briefly symmetry invariance.

State the theory of small oscillations.

M.Sc First Semester Physics (Classical Mechanics) Question Paper 2024 Pdf

Section B
(Long Answer Type Questions)

Note : attempt anyone question each carries 15 marks.

2. Derive Langrange’s equation using D’ Alembert’s principle for conservation and non conservative system.

3. Define generalized coordinates obtain the expression for generalized acceleration, generalized force, generalized potential and generalised momenta.

4. Use the Lagrangian equation of motion to obtain the expression for planetary motion.(Kepler’s Motion).

5. What is hamilton’s principle ? Derive lagrange’s equation with its help for a conservative system. Derive equation of motion for a particle moving under Central force.

Section – C
(Long answer type questions)

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Note : attempt anyone question. Each question carries 15 marks.

6. What is canonical transformation state necessary conditions so that the transformation P = ½ (p² + q²) and Q = tan-1(q/p) is canonical and also find out its generating function.

8. Define the Poisons bracket and discuss its properties so that the Poison bracket is invariant under canonical transformation. i.e.

[x,y]q,p = [ X,Y ] Q,P

8. Obtain Euler’s equation of motion for a rotating body with exist point. Show that the kinetic energy of a rotating body is equal to 1/2w.

9. What do you mean by inertia tensor ? Explain the principle axes and principal movement of inertia. Describe how direction of principal axis and principle movement of inertia of a rigid body can be determined.

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