Question

Derive the expression of linear momentum of a system of particles and prove that the velocity of centre of mass remain constant when total external force on system is zero

Answer 1

your correct answer is here

Answer 2

"Consider if $\quad { F }_{ external }\quad =\quad 0$

Then COM initially at rest, $\Delta { r }_{ cm }\quad =\quad 0$

Therefore $\quad 0\quad =\quad m1\Delta r1\quad +\quad m2\Delta r2$

Hence, $m1\Delta r1\quad =\quad m2\Delta r2$

Similarly, $m1v1=m2v2$

and also m1a1 = m2a2

Consider if COM initially moving

Then, $\Delta { r }_{ cm }$ is not equal to zero

So COM will be moving as per its original motion and then

$\overline { { P }_{ i } } \quad =\quad \overline { { P }_{ f } }$"