State and prove law of conservation of linear momentum.

Law of conservation of Linear momentum:

When no external force acts on the system of several interacting particles, the total Linear momentum of the system is conserved.

The total linear momentum is the sum of linear momentums of all the particles of the system.

Derivation:

Suppose there are n interacting particles having masses and moving with the velocities

The total linear momentum of the system is

If the is the external force acting on the system, then according to the Newton’s second law,

For net external force = 0

Hence in the absence of any external force, the total linear momentum of the system is constant.