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Two stars of mass m(1) and m(2) are part...

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)` respectively, measured from the centre of mass of the system. The magnitude of gravitational force `m_(1)` exerts on `m_(2)` is

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))`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) The situation is as shown in the figure. According to Newton's law of gravitation, 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))`
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