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CBSE Class 9 Answered

derivation of newton's thied law of motion using the 2 nd law
Asked by shresth.senwal | 03 Aug, 2019, 02:16: PM
answered-by-expert Expert Answer
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 = dp1/dt ---------- (i)
=> FAB = dp2/dt---------- (ii)

Adding equations (i) and (ii), we get,
FBA + FAB = dp1/dt + dp2/dt
⇒ FBA + FAB = d(p1 + p2)/dt

If no external force acts on the system, then


d(p1 + p2)/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).
Answered by Thiyagarajan K | 03 Aug, 2019, 03:47: PM

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