A system of binary stars of mass `m_(A)` and `m_(B)` are moving in circular orbits of radii `r_(A)` and `r_(B)` respectively. If `T_(A)` and `T_(B)` are at the time periods of masses `m_(A)` and `m_(B)` respectively then

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)`