7.1.5 Example (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

7.1.5.1 Model: You may view the movement of the two stars using the EJSS below link (require internet) or just below:

1. Run Sim
2. http://iwant2study.org/ospsg/index.php/53

Answer is $\left|F\right|=G\genfrac{}{}{0.1ex}{}{M_1{M}_2}{r^2}=G\genfrac{}{}{0.1ex}{}{2MM}{{\left(3x\right)}^2}=\genfrac{}{}{0.1ex}{}{2}{9}G\genfrac{}{}{0.1ex}{}{M^2}{{\left(x\right)}^2}$