Two identical stars of mass `M` orbit around their centre of mass. Each orbit is circular and has radius `R`, so that the two stars are always on opposite of the circle.
(a) Find the gravitational force of one star on the other.
(b) Find the orbital speed of each star and the period of the orbit.
(c ) What minimum energy would be required to separate the two stars to infinity?

Answer

B, C, D

Explanation

`F = (GM.M)/((2R)^(2)) = (Gm^(2))/(4 R^(2))`

(b) `(GM^(2))/(4R^(2)) = (MV^(2))/(R)`
`:. Nu = sqrt((GM)/(4R))`
`T = (2 pi(R))/(nu) = (2pi R)/(sqrt(GM//4R)) = (4 pi R^(3//2))/(sqrt(GM))` (c ) `W = E_(f) - E_(i) = [U_(f) - U_(i)] + [K_(f) - K_(i)]`
`= [0 - ((-GMM)/(2R))] + [ 0-2 xx (1)/(2) xx M(sqrt((GM)/(4R)))^(2)]`
`= (GM^(2))/(4R)`