Question

state and verify the law of conservation of linear momentum

Answer 1

First off momentum = mass x velocity. You can prove the conservation of momentum (i.e. that it stays the same unless a force acts upon a body) from Newton's laws.

Force = mass x acceleration

Acceleration is the change of velocity over time so:

Force = mass x ((velocity1 - velocity2) / time)

Or:

Force = ((mass x velocity1) - (mass x velocity2)) / time

Because mass x velocity is momentum, we can say:

Force = (momentum1 - momentum2) / time

Or:

Force x time = momentum1 - momentum2

Meaning a change in momentum is caused by force multiplied by time. If there is no force (or no time for it to be applied), the left hand side of the equation is zero, meaning momentum1 = momentum2 (and therefore there is no change in momentum).

Therefore, without a force being applied for a period of time, momentum is conserved.

Answer 2

when no external force on the system then linear momentum is conserved. Acc. to Newton law second law. let system have m1,m2,m3.....mn. and its velocity v1 v2 v3....vn p1 =m1v1 ,p2= m2v2,p3= m3v3,........p= mnvn. total linear momentum of system p= p1+p2+p3+.....pn. f external is directly proportional to dp/st if external force is zero f external= 0 dp/ dt = 0 .means p=constant = p1+ p2+.......+pn.