BSc Physics SEM VI 2018 19 May 2018-19 PHYSICS CLASSICAL MECHANICS Question Paper - Mumbai University | munotes

Questions asked in this paper

• 2. Figures to the right indicate full marks

1. Q1 Attempt any two:
   • (i) State and prove Kepler’s laws of planetary motion. 10 Obtain the equation of motion of a particle of mass ‘m’ as related to the 10 rotating earth. Hence show that the angle between g and ge depends on
   • (iii) Derive an expression for Coriolis theorem. Interpret each term. 10
2. Q2 Attempt any two:
   • (i) What is meant by generalized co-ordinates?) Derive an expression for 10 generalized velocity and generalized kinetic energy Obtain Lagrange’s equation of motion by using D’Alembert’s principle for 10
   • (iii) double pendulum consists of two weightless rods connected to each other 10 and a point of support. The masses m; and are not equal but the length of the rods are equal. Pendulums are free to swing only in one vertical plane Derive the Lagrangian for the system
3. Q3 any two:
   • (1) For fluids, derive the conservation equation for energy in the form of 10 Derive Euler’s equations of motion of a rigid body. Solve these equations for a 10 torque free rotational motion of symmetric body and hence show that the magnitude of the angular velocity vector is a constant
   • (iii) A rigid body is constrained to move about a point which is fixed. Derive an 10 expression for its angular momentum about the instantaneous axis of rotation passing through the fixed point. Hence derive an expression for kinetic energy, Attempt any two:
   • (i) The potential energy of a one dimensional anharmonic oscillator is given by 10 where K is the spring constant and a is anharmonic coefficient. Discuss the potential energy curve for various combinations of K Discuss fixed points of a logistic map, stability of fixed points and periodic 10 attractors. Explain how series of bifurcations lead to chaos when 4 = 3.57
   • (iii) Discuss numerical solutions of Duffing’s equation for y = f =0.5 & 10 f and also explain why the two solutions for even harmonics are different
4. Q5 Attempt any four:
   • (i) Show that when a body moves in a central force field its motion is confined to 5 Find the Coriolis force acting on a body of mass 1kg moving northward with a 5 horizontal velocity of 100 m/s at a place on earth whose colatitudes is N
   • (iii) Define constraints. With good examples, explain holonomic non- 5
   • (iv) Define cyclic coordinate. Which coordinate is called cyclic coordinate. in 5
   • (v) Consider a fluid flow in which velocity is given by, = i x>0. 5 Find the acceleration a(x, t) of the fluid element at position x and time t
   • (vi) body consists of three particles of masses 2, 1 and 4 grams located at 5 of inertia and product of moment of inertia Two very close initial values of x on logistic map are 0.50000 and 0.50002 5 respectively. With A = 4 after 20 iterations the values are 0.08561 and 0.00561 What is phase space Plot the phase space diagram for one 5

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