The centre of mass of a system of two particles of masses $m_{1}$ and $m_{2}$ is at a distance $a_{1}$ from mass $m_{1}$ and at a distance $a_{2}$ from mass $m_{2}$ such that

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Solution

The correct option is A

Referring to diagram the distances of the centre of mass from masses $m_{1}$ and $m_{2}$ respectively are
And $a_{1} = \frac{m_{2} a}{(m_{1} + m_{2})}$
$a_{2} = \frac{m_{1} a}{(m_{1} + m_{2})}$
$\frac{a_{1}}{a_{2}} = \frac{m_{2}}{m_{1}}$
Hence the correct choice is (a).

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