State and explain the law of conservation of momentum of the system of particle. 

Newton's second law for the system of particle,

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

If the sum of external forces acting on the system of particles is zero then

$\frac{d \vec{p}}{d t}=0$

$\therefore d \vec{p}=0, \therefore \overrightarrow{p_{1}}=\overrightarrow{p_{2}}$

Means the linear momentum remains constant.

$(\vec{p}=\text { constant })$

Equation $\vec{p}=$ constant, it is equivalent to three scalar equation as following :

$p_{x}=\mathrm{C}_{1}, p_{y}=\mathrm{C}_{2}, p_{3}=\mathrm{C}_{3}$

where $p_{x^{\prime}} p_{y}$ and $p_{z}$ are the components of linear momentum $\vec{p}$ for respective axis $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ axis and $\mathrm{C}_{1}, \mathrm{C}_{2}$ and $\mathrm{C}_{3}$ are constant.

"When external total force acting on a system of particles is zero, then its total linear momentum remains constant." This is known as conservation of linear momentum.

From $\mathrm{MA}=\overrightarrow{\mathrm{F}}$, here $\overrightarrow{\mathrm{F}}$ is total external force.

If $\overrightarrow{\mathrm{F}}=0$ then $\overrightarrow{\mathrm{MA}}=0$

$\therefore \overrightarrow{\mathrm{A}}=0$

Means, "when total external force on system is zero, the velocity of centre of mass remains constant."

More over $\overrightarrow{\mathrm{A}}=\frac{d \vec{v}}{d t}$ then

If $\overrightarrow{\mathrm{A}}=0$ then $\frac{d \vec{v}}{d t}=0$

$\therefore \vec{v}$ is constant.

Means, total external force on the system is zero, the velocity of centre of mass remains constant.