Question
Two stars of mass $${m_1}$$ 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 $${m_1}$$ 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.
$$\frac{{\left( {{m_1} + {m_2}} \right)}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$$
Answer :
$$\frac{{{m_1}{m_2}G}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$$
Solution :
$$F = \frac{{G{m_1}{m_2}}}{{{r^2}}} = \frac{{G{m_1}{m_2}}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}.$$