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

Consider ure. Suppose the distance of `m_1` from the centre of mass C is `x_1` and that of `m_2` from distance d' towards C so as to keep the centre of mass at C.


then, `m_1x_1=m_2x_2`............i
and `m_1(x_1-d)=m_2(x_2-d')`..........ii
Subtracting ii from i
`m_1d=m_2d'`
or `d'=m_1/m_2d`.