Question

write an expression for the centre of mass of a two particle system?

Answer 1

Ratio of masses is reciprocal of ratio of their distances from CM.

$m_{1}/m_{2}=R_{2}/R_{1} \\R_{2}=L-R_{1}\\R_{1}=m_{2}L/(m_{1}+m_{2})$

$R_{1}$ is distance of CM from $m_{1}$

L is distance of masses from each other