Consider a system of two identical particles having mass m. If one of the particles of mass m is pushed towards the center of mass of the particles through a distance x, by what amount the other particle should move so as to keep the center of mass of particles at the original position?

Explanation

Suppose the distance of mass `m_(1)` from the centre of mass C is `x_(1)` and that of `m_(2)` from C is `x_(2)` Suppose the `m_(2)` is moved through a distance d towards C so as keep the cenre of mass at C.
Then, `m_(1)x_(1)=m_(2)x_(2) " "` ...(1)
and `m_(1)(x_(1)-d)=m_(2)(x_(2)-d')" "` ...(2)
Subtracting (2) and (1)
`m_(1)x_(1)-m_(1)d - m_(1)x_(1)=m_(2)x_(2)-m_(2)d'-m_(2)x_(2)`
`m_(1)d=m_(2)d'`
`d'=(m_(1))/(m_(2))d`