Question

some of the momenta of two object before collision is equal to sum of the momenta after the collision. proof?

Answer 1

By Newton's Second Law,

F(net) = dP/dt
where,momentum is denoted by P
and t is time

So,
If F(net) on the system is zero then the rate of change of momentum with respect to time is equal also zero.

Therefore, we can say that Momentum is constant, because it is not changing with respect to time.

And, hence we can say that even though internal forces act in a considered system , however , Initial total momentum = Final total momentum , however only if net external force on the considered system is zero.

Hope this helps you !

Answer 2

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.