Question

Derive the law of conservation of momentum.

Answer 1

According to Newton's second law of motion, the net external force acting on a body or system is equal to the rate of change of its momentum.
i.e. $F_{ext}=\frac{\Delta P}{\Delta t}$
$F_{ext}$ = Net external force acting on the system

$P$ = Momentum of the system

When $F_{ext}=0$, $\frac{\Delta P}{\Delta t}=0$
$\Rightarrow \Delta P=0$
$\Rightarrow P=constant$
Therefore momentum of the system will be conserved when no net external force acts on the system.