Two stars of mass `m_(1)` and `m_(2)` are parts of a binary star system. The radii of their orbits are `r_(1)` and `r_(2)` respectivey, measured from the centre of mass of the system. The magnitude of gravitational force `m_(1)` exerts on `m_(2)` is

Options

A. `(m_(1)m_(2)G)/((r_(1)+r_(2))^(2))`
B. `(m_(1)G)/((r_(1)+r_(2))^(2))`
C. `(m_(2)G)/((r_(1)+r_(2))^(2))`
D. `(G(m_(1)+m_(2)))/((r_(1)+r_(2))^(2))`

Answer

A

Explanation

The situation is as shown in the figure.
According to Newton's law of gravitational, gravitational force between two bodies of masses `m_(1)` and `m_(2)` is
`F=(Gm_(1)m_(2))/(r^(2))`
Where `r` is the distance between the two masses.
Here, `r=r_(1)+r_(2)`
`F=(Gm_(1)m_(2))/((r^(1)+r_(2))^(2))`