Obtain Newton's second law for system of particle and write it. 

Linear momentum of system of particle

$\vec{p}=m \vec{v}$

Taking differention on both side with time

$\frac{d \vec{p}}{d t}=\mathrm{M} \frac{d \vec{v}}{d t}$ (where $\mathrm{M}=$ constant $)$

$\therefore \frac{d \vec{p}}{d t}=\mathrm{MA}$

$\ldots$ (2)

but $\overrightarrow{\mathrm{MA}}=\overrightarrow{\mathrm{F}}_{\mathrm{ext}}$

From equation (2) and (3),

$\frac{d \vec{p}}{d t}=\overrightarrow{\mathrm{F}}_{\mathrm{ext}}$

is a Newton's second law for the system of particles.

"The external force acting on a system is equal to rate of change of total linear momentum of the system." This is Newton's second law for a system.