Question
A binary system consists of two bodies of masses m1 and m2 separated by distance r. What is the distance of centre of mass from mass m1 and m2?
Solution
Let 
be the position vectors of masses
w.r.t. the centre of mass. 
The moment of mass of the system about centre of mass is zero.
Therefore,
m1r1 + m2r2 = 0
That is,
m1 r1 = - m2 r2 , or
m1 r1 = m2 r2 ... (1)
Also, position vector is given by
R = r1 + r2 ...(2)
On solving (1) and (2), we have 
