two balls of masses 5m and m have radii 2r and r.their center of masses are separated by 10r.they move towards each other under their gravitational force. the distance moved by the centre of smaller sphere when the sheres touch each other?

Answer 1

center of gravity does not move.
5 kg and 1 kg balls
radii 2 and 1
call x = 0 at center of 5 kg ball
Original:
then find CG
5(0) + 1 (10) = 6 (Xcg)
Xcg = 5/3
Final
5 Xbig + 1 Xsmall = 6 (5/3) = 10
Xsmall - Xbig = 3 or Xsmall = Xbig+3
so
5 Xbig + Xbig+ 3 = 10
6 Xbig = 7
Xbig = 7/6
Xsmall = 7/6 + 18/6 = 25/6
so small ball moved
10 - 25/6 = (60-25)/6 = 35/6