1. NEWTONS III LAW OF MOTION: ORIGINAL PROOF A GIFT (ON TEACHERS DAY) FOR ALL MY TRAINEESby Abhishek Alankar on Monday, September 5, 2011 at 10:07pm ·Newtons III Law of Motion states, " To every action there is an equal and opposite reaction andboth take effect on two different bodies and they dont balance each other."Let us consider a system of two bodies having masses M1 and M2 and position vectors R1 and R2.The position vector of the centre of mass of the system will be given byR= M1R1 + M2R2 M1 + M2Differentiating twice with respect to time t, we get the acceleration of centre of mass of the systemA = M1A1 + M2A2 M1 + M2i.e. (M1 + M2)A = M1A1 + M2A2or F = F1 + F2From Newtons II Law of Motion we deduce thatF = 0 (As there are no external forces acting on the system acceleration of its centre of mass A = 0).Therefore,F1 + F2 = 0.i.e. F1 = - F2.This proves the proposition stated by Newtons III Law of Motion.