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

Then `m_(o1)x_(o1)=m_(2)= 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 `