Question

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

• 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. $\frac{G\left(m_{1}+m_{2}\right)}{\left(r_{1} + r_{2}\right)^{2}}$

Answer 1

Answer: (A)

The situation is as shown in the figure.

According to Newtons law of gravitation, gravitational force between two bodies of masses $m_1$ and $m_2$ is
$F = \frac{Gm_{1}m_{2}}{r^{2}}$
where $r$ is the distance between the two masses.
Here, $r= r_{1} + r_{2}$
$\therefore F = \frac{Gm_{1}m_{2}}{\left(r_{1}+r_{2}\right)^{2}}$