## Question 4: State and explain law of conservation of linear momentum for an isolated system of bodies.

### Conservation of momentum

The law of conservation of momentum for an isolated system states that for an isolated system, the total linear momentum remains constant.

If and are the momentums of the isolated system before and after the collision, then according to the law of conservation of momentum,

Isolated system:

If a system of two or more than two bodies which can interact with one another but no external agency can exert force on them, then such a system is called isolated system.

No such system exists in practice. However, if the mutual interaction of two bodies is much greater than the interaction with other external bodies, then such a system can be treated as an isolated system.  If there is no external force applied to a system (that is the system is isolated), the linear momentum of that system remains constant with time.

Explanation: Consider two bodies of masses m1 and m2 moving with velocities v1 and v2, respectively, in the same direction and same line. See the diagram below. Now when a collision happens between them, they exert forces F21 and F12 on one another during the collision which change their velocities. Let u1 and u2 are their respective new velocities after collision. Now, we know that

Force = rate of change of momentum

Therefore, force on first body is the rate of change of its momentum, Force on second body is the rate of change of its momentum, Apply Newton’s third law, the forces of action and reaction are equal and opposite.    Momentum of the system after collision = Momentum of the system before collision

This means total momentum of an isolated system is conserved.