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 be moved so as to keep the centre of mass at the same position?

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$\frac{m_{2}}{m_{1}} d$

$\frac{m_{1}}{m_{2}} d$

$d$

$\frac{m_{1}}{m_{1} + m_{2}} d$

answer is A.

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Detailed Solution

For the centre of mass to not move

$m_{1} Δ x_{1} + m_{2} Δ x_{2} = 0$

$\Rightarrow m_{1} d + m_{2} ∆ x_{2} = 0$

$\Rightarrow ∆ x_{2} = - \frac{m_{1} d}{m_{2}}$

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