Question

State & prove the law of
conservation of momentum​

Answer 1

Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force.  

Proof:

Consider a body of mass m1  moving with velocity  U1,  striking against another body of mass m2  moving with velocity  U2.

Let the two bodies remain in contact with each other for a small interval "delta t".

Let F12  be the average force exerted by mass m1 on m2, and let F21  be the force on m2 due to m1.

Let v1 and v2 be the velcoities of two bodies after collision.

Momentum of mass m1 before collision=m1u1

Momentum of mass m2 after collision=m2u2

Momentum of mass m1 after collision=m1v1

By using the definition of impulse, change in momentum of mass m1 is,

(refer figure).