Question

Where does centre of mass lie when 1 particle is heavier than the other?

Answer 1

Denote the two particles as M1 and M2 and their separation as x. Let a be the distance of m1 from the center of mass. The center of mass is the point where the moments of the two masses are equal. Thus M1a = M2(x-a). Hence M1a + M2a = M2x. Therefore a = M2x/(M1 + M2)