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Question

Derive Newton's third law of motion from law of conservation of momentum.

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Solution

Consider an isolated system in which two bodies A and B collide. Let F1 be the force exertedby the body A on B for time t. Let F2 be the force exerted by body B on A for time t.Now, change in linear momentum=Force×timeChange in linear momentum of B=F1×tChange in linear momentum of A=F2×tTotal change in linear momentum of A and B=F1×t+F2×tAs no external force acting on the system, therefore according to newton's second law of motion, the total change in linear momentum of the system is zero.F1t+F2t=0F1t=-F2tF1=-F2

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