Hamiltonion Equation-Classical and Relativistic Mechanics-Exam Paper, Exams of Classical and Relativistic Mechanics

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Final Exam (Classical and Relativistic Mechanics) Dated; 08-04-2011 Duration: 3 hours / Q1. Using the symmetric Hamiltonian equations and the concept of integra- tion, show that H=pq-L Jf ne. Q2. Show that the electromagnetic wave equation Oro a7 Os ad 1 d¢ Ox2 | Oy? 0? c* Ot? = 0 Me of this result? Q3. A huge missile explodes and divides into two equal parts, which take off with velocities c/2, one to the right and the other to the left. The piece that moves to the right again gets divided into two, by an explosion such that with respect to its own rest frame the resulting two pieces take off with velocities c f2 to the right and left. Calculate the velocities of the last Hm pieces with respect C@) (5) is Lorentz invariant. Can oF a statement about the importance the aarit If a and a/ are the velocities of a particle in frame S and S/ which ar moving with velocity v relative to each other, show that ae _ 0-0-8) - c? 1— (}of) Write a note on any two of the following questions. 1) Relativity of Simultaneity ~~ 2) Causality and Maximum signal velocity 3) Foucault’s Pendulum (7.5, 7.5) Vt v docsity.com