A double star is a system of two stars of masses `m` and `2m`, rotating about their centre of mass only under their mutual gravitational attraction. If `r` is the separation between these two stars then their time period of rotation about their centre of mass will be proportional to

Options

A. (i),(iii)
B. (i),(iv)
C. (ii),(iii)
D. (ii),(iv)

Answer

B

Explanation

`r_(1)=(2mL)/(m+2m)=(2L)/3`
`(G.2m.m)/(L^(2))=momega^(2)r_(1) = m omega^(2).(2L)/3`
`omega=sqrt((3Gm)/(L^(3)))`
`T=(2pi)/(omega)=(2piL^(3//2))/(3sqrt(Gm)), T prop L^(3//2), T prop m^(-1//2)`