Obtain Newton's second law for a system of particles and write its statement.

(N/A) The total linear momentum of a system of particles is given by $\vec{p} = M\vec{v}_{cm}$,where $M$ is the total mass of the system and $\vec{v}_{cm}$ is the velocity of the centre of mass.
Taking the derivative with respect to time $t$ on both sides:
$\frac{d\vec{p}}{dt} = M \frac{d\vec{v}_{cm}}{dt}$
Since the acceleration of the centre of mass is $\vec{a}_{cm} = \frac{d\vec{v}_{cm}}{dt}$,we have:
$\frac{d\vec{p}}{dt} = M\vec{a}_{cm}$
According to the motion of the centre of mass,the net external force acting on the system is $\vec{F}_{ext} = M\vec{a}_{cm}$.
Therefore,substituting this into the equation,we get:
$\frac{d\vec{p}}{dt} = \vec{F}_{ext}$
This is Newton's second law for a system of particles.
Statement: The external force acting on a system of particles is equal to the rate of change of the total linear momentum of the system.