Assertion : The centre of mass of system of  n particles is the weighted average of the  position vector of the n particles making up  the system.
Reason : The acceleration of the centre of mass of a system is independent of internal forces

The centre of mass of system of  n particles is the weighted average of the  position vector of the n particles making up  the system.

$\overrightarrow{\mathrm{r}}=\frac{{\mathrm{m}}_1\overrightarrow{{\mathrm{r}}_1}+{\mathrm{m}}_2\overrightarrow{{\mathrm{r}}_2}+{\mathrm{m}}_3\overrightarrow{{\mathrm{r}}_3}+\dots \dots \dots {\mathrm{m}}_{\mathrm{n}}\overrightarrow{{\mathrm{r}}_{\mathrm{n}}}}{{\mathrm{m}}_1+{\mathrm{m}}_2+{\mathrm{m}}_3+\dots \dots \dots {\mathrm{m}}_{\mathrm{n}}}$

The acceleration of the centre of mass of a system is independent of internal forces. It depends on external force and mass of system.

${\mathrm{a}}_{\mathrm{cm}}=\frac{{\mathrm{F}}_{\mathrm{ext}}}{{\mathrm{m}}_{\mathrm{sys}}}$