The law of momentum conservation can be stated as follows. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.According to newton’s 2^{nd} law, the rate of change of momentum is equal to external force applied.

So, F_{external} = F_{resultant} = dp/dt

We already know that change of momentum of a body is due to internal forces is equal to “0”, because the internal forces are mutual forces and cancel out each other.

So, F_{external} = dp/dt

When the external force doesn’t act on a body

dp/dt = 0

So, therefore P is a constant.

So, we can also say that when only internal force are acting momentum of a system is conserved.

This is called conservation of momentum.