MSc Physics (Electronics I) SEM III 2022 2023 Dec 2023 PHYSICS CLASSICAL MECHANICS Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 (a) Attempt any one: - 8 marks
   • (i) Show that the total angular momentum of system of particles about a point is the angular momentum of motion concentrated at the center of mass plus the angular momentum of motion about the center of mass
   • (ii) Obtain Lagrange’s equation of motion using D’Alembert’s principle
   • (b) Attempt any one: - 4
   • (i) What are constraints? Explain non-holonomic constraints
   • (ii) Derive the Lagrange’s equation for a simple pendulum
2. Q2 (a) Attempt any one: - 8 marks
   • (i) and prove the Viral theorem and show that how it leads to ideal gas
   • (ii) Derive differential equation of orbit for a particle under central force
   • (b) Attempt any one: - 4
   • (i) Explain the term impact parameter and the differential cross-section
   • (ii) Show that the central force motion is restricted to plane
3. Q3 (a) Attempt any one: - 8 marks
   • (i) For a particle performing small oscillations near the minima of some potential function, derive the Lagrange equations of motion
   • (ii) are Legendre transformations? Derive Hamilton’s equations from
   • (b) Attempt any one: - 4
   • G) Explain forced and damped oscillations
   • (ii) | Write down the steps to find the Hamiltonian from the Lagrangian
4. Q4 (a) Attempt any one: - 8 marks
   • (i) What is generating function F? For F = F,(q, Q,t) derive expressions for p;, P; and have their usual meanings.)
   • (ii) Show that Poisson Brackets remain invariant under Canonical
   • (b) Attempt any one: - 4
   • (i) Show that the following transformation is canonical
   • (ii) | Write down the direct conditions for a transformation to be restricted
5. Q5 Attempt any four: - 12 marks
   • (a) short note on degrees of freedom
   • (b) Show that the shortest distance between two points in a plane is a straight line
   • (c) State Kepler’s laws of planetary motion
   • (d) Explain bounded motion and unbounded motion and give examples
   • (e) With proper example, explain the concept of cyclic coordinates
   • (f) | Show that Vij is symmetric
   • (g) Write Hamilton’s equations of motion in symplectic form. Explain the terms involved in it
   • (h) Show that [A, BC] = [A, + B[A, C]

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