BSc Sem VI 2014 2015 2015 Physics Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 (a) Wet the equation of motion of a particle in a central field. Solve it to get equation of orbit, for inverse Square force field. Explain different orbits 10 marks
   • (ii) State Coriolis theorem. Give interpretation of various terms in 10 the equation. Explain the effect of centrifugal force with respect to rotating earth
   • (b) Attemptany one :— Kepler’s laws of planetary motion. Prove that the areal 5 velocity of planet ina orbit is constart
   • (ii) Explain the effect of Coriolis force on a particle moving in a 5 horizontal plane in the northern hemisphere near. the earth
2. Q2 (a) Attem t any one Derive Lagrange’s of motion in Several diamensions 10 with no constraints imposed,
   • (ii) Explain how the forces of Constraints are determined used 10 Lagrangian formulation. Illustrate the same taking Atwood’s machine as ay, example,
   • (b) Attempt any one Lagr for a simple pendulum and
   • ii) its motion Without constraint Attempt any one -— S theorem anq discuss how it represents the 10 On law of for a fluid A rigid body is constrained to move about a point whichis 10 axis of rotation passing through the fixed point Hence derive an expression for kinctic energy of the body and express in terms of angular momentum
   • (b) Attempt any one :— In case of a fluid moving with velocity show that 5 Using this, show that Lagrangian for the top is given by Find equation of motion of the top
   • (a) Attempt any one :— What do you mean by fractals dimension? Show the construction 10 of cantor set and Sierpinski gasket. Hence find fractal dimension in each case
   • (ii) The reduced Duffing’s equation of motion for an anharmonic 10 oscillator is Discuss its numerical solution considering y = 0:1 with special reference to sub harmonic resovances and hysteresis for f=3; period - 2 orbits for f=20 anc leading to chaos for £25
   • (b) Attempt any orc :— graphical illustration of potential energy of an anharmonic constructed using hard spring and subjected to a the motion in each case, Explain scale invariance in the Poincare section having 5 bifurcations leading to chaos. Hence explain the Feigenbaum
   • a) Attempt any one
   • (i) The eccentricity of planet orbit about the sun is 0.6. F ind the 4 ratio of lengths of major to minor axes the time taken by the plane of oscillations endulum at colatitude to turn through in the northern
   • (b) Attempt any one :— a short note on constraints. 4 Write a short note on constants of motion and ignorable co
   • (c) Attempt any one Consider a fluid flow in which the velocity is given by 4 x>0. Find the acceleration a(x,t) of the fluid element at position x and time t. Is the flow a rigid body, the inertia tensor is given by 4 Find the principal moment of inertia for the body > (d) Attempt any one :—
   • (i) Write a Henon map. 3
   • (ii) Discuss the chactic behavior of Lyapunov exponent

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