Question

derive the third newton's law of motion

Answer 1

Consider an isolated system of two bodies A & B mutually interacting with each other, provided there is no external force acting on the system. Let FAB, be the force exerted on body B by body A and FBA be the force exerted by body B on A. Suppose that due to these forces FAB and FBA, dp1/dt and dp2/dt be the rate of the change of momentum of these bodies respectively. Then, FBA = d p 1 dt ---------- (i) => FAB = d p 2 dt ---------- (ii) Adding equations (i) and (ii), we get, FBA + FAB = d p 1 dt + d p 2 dt ⇒ FBA + FAB = d( p 1 + p 2 ) dt If no external force acts on the system, then d( p 1 + p 2 ) dt = 0 ⇒ FBA + FAB = 0 ⇒ FBA = - FAB---------- (iii) the above equation (iii) represents the Newton's third law of motion (i.e., for every action there is equal and opposite reaction)...

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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