Motion of the Centre of Mass

Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass :- Show (dL')/(dt)=(sumr_i') xx (dp')/(dt) Further, show that (dL')/(dt)= tau'_(ext) where tau'_(ext) is the sum of all external torques acting on the system about the centre of mass.

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vec L = L = vec L + vecM R xx vecV where vec L = Sigma vecr_i xx vecp_i is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vecr_i = vecr_i - vecR , rest f the notation is the standard notation used in the chapter. Note vecL and vecMR xx vecV can be said to be angular moemnta respectively about and of the centre of mass of the system of particles.

Two bodies A and B initially at rest are attrached towards each other due to gravitation. Given that A is much heavier. Than B . Which of the followings correctly describes the relative motion of the centre of mass of the bodies ?