question_answer

Two stars of mass \[{{\operatorname{m}}_{1}} and {{m}_{2}}\]are parts of a binary system. The radii of their orbits are \[{{r}_{1}} and {{r}_{2}}\]respectively, measured from the C.M. of the system. The magnitude of gravitational force \[{{\operatorname{m}}_{1}}\]exerts on \[{{m}_{2}}\]is

A) \[\frac{{{m}_{1}}{{m}_{2}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\]

B) \[\frac{{{m}_{1}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\]

C) \[\frac{{{m}_{2}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\]

D) \[\frac{\left( {{m}_{1}}+{{m}_{2}} \right)}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\]