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# EIILM UNIVERSITY, SIKKIM TERM END EXAMINATIONS, FEBRUARY -2012 BACHELOR OF SCIENCE (PCB), 1 YEAR MECHANICS AND RELATIVITY Time -3 Hours Max Marks: 60...

A 0.3 kg mass is attached to a spring and oscillator at 2 Hz with a Q of 60. Find
the damping constant
EIILM UNIVERSITY, SIKKIM TERM END EXAMINATIONS, FEBRUARY -2012 BACHELOR OF SCIENCE (PCB), 1 YEAR MECHANICS AND RELATIVITY Time -3 Hours Max Marks: 60 Note: - Attempt any FIVE questions. All questions carry equal marks. 1. Four particles of mass 1, 2, 3 and 4g respectively, move under the influence of a force field so that their position vectors (in cm) are defined by r1 = 2t2i ˆ + 4t j ˆ + 5tk ˆ r2 = 3ti ˆ – 2t2k ˆ r3 = t2i ˆ + 2tk ˆ r4 = 4ti ˆ – 2t j ˆ Find the equation for centre of mass. 2. Calculate the inertia tensor for a cube of mass M and each side a, with respect to the coordinate system having origin at the centre of the cube, and axes parallel to the forces. 3. A 0.3 kg mass is attached to a spring and oscillator at 2 Hz with a Q of 60. Find the damping constant. 4. Show that if a collision is elastic in one frame of reference, it is elastic in all inertial frames. 5. Show that two successive Lorentz transformations commute, and are equivalent to one Lorentz transformation. 6. Show that in a system obeying Maxwell-Boltzmann statistics, the number of particles each having energy 1/2 kT is maximum. 7. Four distinguishable particles are distributed among 2 energy levels with 2 particles in each level. The energy levels have statistical weights 3 and 4. Find the total number of microstates.
8 What is the difference between inertial frames of reference and non-inertial frames of reference ?

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