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

Answer

D

Explanation

In binary star system angular velocity are qual hence the time period of both the stars are equal.
`omega = (2pi)/(T_(A)) = (2pi)/(T_(B))`
`therefore T_(A) = T_(B)`