Consider a two particle system with the particles having masses `m_1 and m_2`. If the first particles pushed towards the centre of mass through a distance d, by what distance should the second particle be moved so as the keep the centre of mass at the same position?

Explanation

Consider figure suppose the distance of `m_(1)` from the centre of mass `C` is `x_(1)` and that of `m_(2)` from `C` is `x_(2)`. Suppose mass `m_(2)` is moved through a distance `d'` towards `C` so as to keep the centre of mass at `C`.

Then `m_(1)x_(1)=m_(2)x_(2)` .......i
and `m_(1)(x_(1)-d)=m_(2)(x_(2)-d')`...........ii
Subtracting eqn ii and from eqn i we get
`m_(1)d=m_(2)d'` or `d' =(m_(1)//m_(2))d`