A binary star system consists of two stars of masses `M_(1)` and `M_(2)` revolving in circular orbits of radii `R_(1)` and `R_(2)` respectively. If their respective time periods are `T_(1)` and `T_(2)`, then

Options

A. `T_(1)gt T_(2)` if `R_(1)gt R_(2)`
B. `T_(1)gt T_(2)` if `M_(1)gt M_(2)`
C. `T_(1)=T_(2)`
D. `(T_(1))/(T_(2))=((R_(1))/(R_(2)))^(3//2)`

Answer

C

Explanation

In a binary star system, there are two stars moving under their mutual gravitational force of attraction. Their angular velocities are equal and hence their periodic times are also equal. `[because omega = (2pi)/(T)]`
`therefore T_(1)=T_(2)`