A double star system consists of two stars `A` and `B` which have time periods `T_(A)` and `T_(B)`. Radius `R_(A)` and `R_(B)` and mass `M_(A)` and `M_(B)`. Choose the correct option.

Options

A. `(T_(A))/(T_(B))=((r_(A))/(r_(B)))^(3/2)`
B. `T_(A)gtT_(B)` (if `r_(A)gtr_(B))`
C. `T_(A)gtT_(B)` (if `m_(A)gtm_(B))`
D. `T_(A)=T_(B)`

Answer

D

Explanation

If the binary starts are rotaitng about their common centre of mass, then they have to be on the same line all the time, otherwise the centre of mass will be changing. Their angular velocities have to be the same although in the same time, the smaller mass will describe a bigger circle.
But as `omega=(2pi)/T`, so `T_(A)=T_(B)`