rare and original proof of newton's III law of motion

1. NEWTON'S III LAW OF MOTION: ORIGINAL PROOF
A GIFT (ON TEACHERS' DAY) FOR ALL MY TRAINEES
by Abhishek Alankar on Monday, September 5, 2011 at 10:07pm ·
Newton's III Law of Motion states, " To every action there is an equal and opposite reaction and
both take effect on two different bodies and they don't 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 by
R= M1R1 + M2R2
M1 + M2
Differentiating twice with respect to time t, we get the acceleration of centre of mass of the system
A = M1A1 + M2A2
M1 + M2
i.e. (M1 + M2)A = M1A1 + M2A2
or F = F1 + F2
From Newton's II Law of Motion we deduce that
F = 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 Newton's III Law of Motion.