Nalanda Open University 2009 B.Sc Physics Final , Bachelor Science, Part-III -V - Question Paper
Final Examination, 2009 Bachelor Science, Part-III Paper-V (Physics)
Final Examination, 2009 Bachelor Science, Part-III Paper-V (Physics)
Time: 3.00 Hrs. Full Marks: 75
Answer any Five Questions. All questions carry equal marks
1. Solve the wave equation by the method of Separation of variables.
2. Solve the equation y"(x) - y(x) = 0 by power series method.
3. Show that ex (cosy + i siny) is an analytic function and find its derivative.
4. State and prove Laurent theorem.
5. Describe the algebraic properties of tensors of arbitrary rank using both covariant and contravariant indices.
6. Deive Euler - Lagrange equation and hence discuss the Brachistochrone problem.
7. Set up Euler's equations of motion of a rigid body and hence discuss the motion of a symmetrical top.
8. What are Poisson brackets? State and prove some of its important properties.
9. Prove that the Poisson bracket of two constants of motion is itself a constant of the motion even when the constants depend on time explicitly.
10. Define action and angle variables for a system with one degree of freedom. Apply their theory to find the time period of small oscillations.
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