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B.Sc. (Hons) Physics III (Third) Semester Examination 2013-14 Course Code: BAS306 Paper ID: 0983208 Classical Physics Time: 3 Hours Max. Marks: 70 Note: Attempt six questions in all. Q. No. 1 is compulsory. 1. a) b) c) d) e) f) g) h) 2. a) b) Answer any five of the following (limit your answer to 50 words). (4x5=20) What are generalized coordinates? Distinguish a system on the basis of time dependence of generalized coordinates. Show that for a single particle with constant mass, the differential equation for kinetic energy is dT F .v . where T is kinetic energy dt Using Hamilton’s principle show that the shortest distance between two points is a straight line joining them. Explain the condition for a transformation to be canonical. Show that the transformations Q p and P q are canonical transformations. Obtain Hamilton’s equations for a charged particle moving in an electromagnetic field. Show that the central force motion of two bodies about their center for mass can be reduced to an equivalent one body problem. Using Poisson brackets, obtain Jacobi identity. Derive Lagrange’s equations in presence of non conservative forces. (5) Explaining the velocity dependent potential. Write the expression for the velocity dependent potential of electromagnetic field. (5) 3. Apply Hamilton’s principle to derive Lagrange’s equation. Using Hamilton’s principle, find the equation of motion of one dimensional harmonic oscillator. (10) 4. Discuss the advantages of using a Lagrangian for the description of a system. Use Lagrangian to establish analogy between an electrical and a mechanical system. (10) 5. What are non-holonomic systems? Apply the Lagrange’s method of undetermined multipliers to the problem of a hoop rolling down an inclined plane without slipping. (10) 6. What is the objective of Legendre transformation? Derive Legendre transformation and apply it to generate a thermodynamic quantity. (10) 7. Define canonical transformations and generating function. Obtain the transformation equations corresponding to various generating functions. (10) 8. Explain action angle variable. Obtain the solution of harmonic oscillator problem by action angle variable. (10)