Question

Derive law of conservation of linear momentum in case of a colliding bodies

Answer 1

Alternatively, it states that if net external force acting on a system is zero, the total momentum of the system remains constant.

Proof:

Let us consider a particle of mass ‘m’ and acceleration ‘a’. Then, from 2nd law of motion,

Law of Conservation of Linear Momentum

If no external force acts on the body then, F=0,

Law of Conservation of Linear Momentum

Therefore, ‘P’ is constant or conserved.

(Note: If the derivative of any quantity is zero, it must be a constant quantity.)

Answer 2

Newton's third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum. ... B=m_{2}(v_{2}-u_{2}) (change in momentum of particle B)