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. `r^(3//2)`
B. r
C. `m^(1//2)`
D. `m^(-1//2)`

Answer

A, D

Explanation

Motion of m
`momega^(2)((2r)/(3))=(Gm(2m))/(r^(2))impliesT=(2pi)/(omega)=2pisqrt((r^(3))/(3Gm))`
`thereforeTpropr^(3//2)` and `Tpropm^(-1//2)`