Two particles of masses `2m` and `3m` are placed at separation `d` on a smooth surface. They move towards each other due to mutual attractive force. Find (a) acceleration of c.m. (b) Velocity of c.m. when separation between particles becomes `d//3`. ( c) At what distance from the initial position of mass `2m`, the particles collide.

Explanation

(a) In a absence of any external force the acceleration of CM is zero.
`F_(ext) = 0`, `a_(CM) = 0`
(b) Initially the particles are at rest `v_(1) = v_(2)=0`, therefore, `v_(CM) =0`. Since `F_(ext = 0`, the velocity of CM is constant and hence `v_(CM` is always zero whenever the separation becomes `d//2,d//3` etc.
(c) First, locate the CM
`x_(CM) = (2m xx 0 + 3m xx d)/(2m + 3m)` = 3d/5`

Since, the CM is at rest, its position is fixed, hence particles will meet at CM i.e, at distance `3d//5` from A.