In a binary star system one of the stars has mass equal to mass of sun `(M)`. Separation between the stars is four times the average separation between earth and sun. Mass of the other star so that time period of revolution of the stars each other is equal to one earth year is

Options

A. `31M`
B. `63M`
C. `M`
D. `2M`

Answer

B

Explanation

For earth `T=2pisqrt((r^(3))/(GM))`………i
For binary start system `T=2pisqrt(((4r)^(3))/(G(M+M^(')))`…….ii
From i & ii `M^(')=63M`