Binary stars of comparable masses rotates under the influence of each other's gravity at a distance `[(2G)/(omega^(2))]^(1//3)` where `omega` is the angular velocity of each of the system. If difference between the masses of two stars is `6` units. Find the ratio of the masses of smaller to bigger star.

Options

A. `4:10`
B. `1:7`
C. `2:8`
D. `3:9`

Answer

B

Explanation

`m_(1)r_(1)=m_(2)r_(2)=(m_(2)r)/(m_(1)+m_(2))......(i)`
`m_(1) r_(1)omega^(2)=(Gm_(1)m_(2))/(r^(2)) omega^(2)=(G(m_(1)+m_(2)))/(r^(3))`
From (i) or `r =[(G(m_(1)+m_(2)))/(omega^(3))]^(1//3)`
`(m_(1)+m_(2))^(1//3)=2m_(1)+m_(2)=8`
and `m_(2)-m_(1)=6` (given)
`(m_(1))/(m_(2))=1/7`