Question

How to prove newton's third law from the second law?

Answer 1

Consider an isolated system of 2 bodies A & B. An isolated system means where there is no external force acting.Now let F be the force acting on B by A & F be the force acting on A by B.Now rate of change of momentum of A =dpA/dt and rate of change of momentum of B =dpB/dt

thus FAB=dpB/dt (i)......

FBA=dpA/dt (ii)........

Adding 1 and 2 we get FAB+FBA=dpB/dt+dpA/dt =d(pB+pA)/dt

But if no force is applied momentum will also be 0 because no velocity will be there so rate of change of momentum will also be 0

thus d(pA+pB)/dt=0

therefore FAB+FBA=0

or,FAB=-FBA

(3RD LAW OF MOTION)

hope this answer helps!!!

Answer 2

$\textbf{Action - Reaction Law :}$


It is Newton's Third Law.

According to it, for every action there is equal and opposite reaction. [Equal in Magnitude but opposite in Direction.]

[DERIVATION is in Attachment !!]

$\textbf{F12 (vector) = - F21 (vector)}$

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