Question

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

Answer 1

Correct Answer - B

`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)`