A pair of stars rotates about their center of mass. One of the stars has a mass M and the other has mass m such that M = 2m. The distance between the centers of the stars is d (d being large compared to the size of either star).
(i) The period of rotation of the stars about their common center of mass (in terms of d, m, G.) is
Text Solution
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(i) d (ii)b (iii)b
Sol. (i) to (iii)
Let the angular speed of revolution of both stars be ω about the common center, that is, center of mass
of system.
The centripetal force on star of mass m is
mv 2 
= 
. Solving we get T= 
The ratio of angular momentum is simply the ratio of moment of inertia about center of mass of system.
Similarly, The ratio of kinetic energy is simply the ratio of moment of inertia about center of mass of
system.
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