BABSc, B.Com & BCA Questions _III - Nalanda Open University
BABSc, B.Com & BCA Questions _III - Nalanda Open University
BABSc, B.Com & BCA Questions _III - Nalanda Open University
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<strong>Nalanda</strong> <strong>Open</strong> <strong>University</strong><br />
Annual Exam-2010,<br />
Bachelor of Science (Physics) Hons, Part-<strong>III</strong><br />
(Mathematical Physics and Classical Mechanics)<br />
Paper-V<br />
Time: 3 Hrs Full Marks: 75<br />
Answer any five questions. All questions are of equal marks.<br />
1. Find the solution of Laplace’s equation<br />
∇ 2 φ = 0<br />
In spherical polar co-ordinates.<br />
2. Using the method of separation of variables, solve the following equation.<br />
∂u<br />
∂u<br />
= 2 + u<br />
∂x<br />
∂t<br />
3. Solve the following equation by power series method.<br />
2<br />
d y( x)<br />
− y( x)<br />
= 0<br />
2<br />
dx<br />
1+<br />
2i<br />
4. Express 1−<br />
3i in polar form.<br />
5. State and prove Cauchy’s Residue Theorem.<br />
6. Using Lagrange’s equation, discuss the symmetries and Conservation Laws and<br />
hence show that total energy of the system remains conserved.<br />
7. Discuss principal moment of inertia and Principal axis for the rigid body. Define<br />
symmetrical, asymmetrical and spherical top.<br />
8. (a) Prove that the transformation P = ½ (p 2 + q 2 ), Q = tan -1 ( q / p ) is Canonical.<br />
(b) Show that the generating function for the transformation<br />
1<br />
p<br />
Q and q PQ 2<br />
is F q<br />
= = =<br />
Q<br />
9. Establish Hamilton – Jacobi’s equation.<br />
10. Set up action- angle variables for the system of one dimensional harmonic oscillator<br />
and hence find the frequency of oscillation.<br />
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