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Consider a two particle system with part...

Consider a two particle system with particles having masses `m_(1)andm_(2)`. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

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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`.
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