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Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively, measured from the centre of mass of the system. The magnitude of gravitational force $m_1$ exerts on $m_2$ is
$\frac{{{m_1}{m_2}G}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
$\frac{{{m_1}G}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
$\frac{{{m_2}G}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
$\frac{{G({m_1} + {m_2})}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
Solution
The situation is as shown in the figure.
According to Newton's law of gravitation,
gravitational force between two bodies of masses
$\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ is.
$\mathrm{F}=\frac{\mathrm{Gm}_{1} \mathrm{m}_{2}}{\mathrm{r}^{2}}$
where $\mathrm{r}$ is the distance between the two masses.
Here, $\mathrm{r}=\mathrm{r}_{1}+\mathrm{r}_{2}$
$\therefore \quad \mathrm{F}=\frac{\mathrm{Gm}_{1} \mathrm{m}_{2}}{\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)^{2}}$
