Example 3 (N09/I/16) Binary Stars 

Two stars of mass M and 2M, at a distance 3x apart, rotate in circles about their common centre of mass O.
The gravitational force acting on the stars can be written as $\genfrac{}{}{0.1ex}{}{kG{M}^2}{x^2}$ .
What is the value of k?
A  0.22             B  0.50                C  0.67             D  2.0