Answer:
As shown in Fig. consider a system of two particles of masses \[{{m}_{1}}\]and \[{{m}_{2}}\] situated at points A and B respectively. Suppose the origin O of the frame of reference coincides with their centre of mass. 
If \[{{\vec{r}}_{1}}\] and \[{{\vec{r}}_{2}}\] are the position vectors of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] with respect to the centre of mass, then \[{{m}_{1}}{{\vec{r}}_{1}}+{{m}_{2}}{{\vec{r}}_{2}}=({{m}_{1}}+{{m}_{2}})\vec{O}=0\] or \[{{\vec{r}}_{1}}=-\frac{{{m}_{2}}}{{{m}_{1}}}{{\vec{r}}_{2}}\] or \[|{{\vec{r}}_{1}}|=\frac{{{m}_{2}}}{{{m}_{1}}}|{{\vec{r}}_{2}}|\] or \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] Hence the centre of mass of two particles divides the line joining the two particles in the inverse ratio of their masses.
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