Question

State and derive he law of conservation of momentum.

Answer 1

according to the law of conservation of momentum

When two bodies act upon one another their total momentum remains constant provided no external forces are acting.

m1u1+m2u2=m1v1+m2v2

Answer 2

The law of conservation of linear momentum states that if no external forces act on the system of two colliding objects, then the vector sum of the linear momentum of each body remains constant and is not affected by their mutual interaction.

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.)

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