Question

State the Law of Conservation of Momentum. Deduce this from Newton's second law
of motion?

Answer 1

$\huge{\underline{\underline{\sf \: {Answer}}}}$

Law of conservation of momentum. This law states that if a number of bodies are interacting with each other i.e., exerting forces on each other), their total momentum remains conserved before and after the interaction, provided there is no external force acting on them.

Derivation from Newton's second law of motion. Let p1 and p2 represent the sum of momenta of a group of objects before and after the collision, respectively. Let t be the time elapsed during the collision.

According to Newton's second law of motion,

External force Rate of change of momentum

$\implies \huge \sf f = \frac{p2 - p1}{t}$

Hence in the absence of an external force, the total momentum of a group of objects remains unchanged