State the law of conservation of momentum.

Explanation

Consider two small spheres A and B of masses `m_(A)` and `m_(B)` moving in the same direction along a straight line with velocities and up UAU They collide with each other after some time. According to Newton.s third law of motion, at the time of impact the spheres exert equal in magnitude and opposite in direction forces on each other. They collide for time t.

Let their velociteies be `v_(A)` and `V_(B)` after collision Force exerted by sphere A on sphere B is `F_(AB)`=rate of change of momentum of sphere B
`(m_(B)(v_(B)-u_(B)))/(t)`.........(1)
Force exerted by sphere B on sphere A is `F_(BA)` =rate of change of momentum of sphere A
`=(m_(A)(v_(A)-u_(A)))/(t)`
Now using Newton.s third law of motion
`F_(AB)=-F_(BA)`
From (1)and (2).
`therefore (m_(B)(v_(B)-u_(B)))/(t)=-(m_(A)(v_(A)-u_(A)))/(t)`
`therefore (m_(B)v_(B)-m_(B)u_(B))/(t)=-(m_(A)(v_(A)-u_(A)))/(t)`
`therefore m_(B)v_(B)-m_(B)u_(B)=-m_(A)v_(A)-m_(A)u_(A)`
`therefore m_(A)v_(A)+m_(B)v_(B)=m_(A)u_(A)+m_(B)u_(B)`
From this,we conclude that when two bodies collide with each other,their total momentum after collision is equal to their total momentum beore collision .PRovided that no other forces at upon them.