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

Explanation

Consider figure. Suppose the distance of m1 from the centre of mass C is `x_(1)` and that of `m_(2)` from C is `x_(2)` . Suppose the 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 (ii) from (i)
`m_(1)d=m_(2)d'`
or, `d'=(m_(1))/(m_(2))d`,