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. if `T_(A)gtT_(B)` then `R_(A)gtR_(B)`
B. if `T_(A)gtT_(B)` then `M_(A)gtM_(B)`
C. `((T_(A))/(T_(B)))^(2)=((R_(A))/(R_(B)))^(3)`
D. `T_(A)=T_(B)`

Answer

D

Explanation

Figure shows a binary star system:
The gravitaional force of attraction between the stars will provide the necessary centripetal forces. In this case angular velocity of both stars is the same. Therefore time period remains the same.
`(omega=(2pi)/(T))`