Question

prove that centre of mass of two particles divides the line joining the particles in inverse ratio of their masses

Answer 1

Let us consider a two particle system of masses m1 and m2at the points A and B respectively.

Consider point C as the centre of mass of system. If  and  are the position vector of masses m1 and m2, the position of the centre of mass will be given as-



If the origin of co-ordinate system is shifted at the centre of mass C of the system, then

.

 Using eq. (1) we get



 

Hence, the centre of mass of two particle system divides the line joining the particles in the inverse ratio of their masses.

Answer 2

Answer:

here is the complete derivation,