Consider a binary system of stars X of mass `M_(x)` and Y of mass `M_(y)` Their masses are different and they revolve
about their centre of mass. Separation between the stars is R. The distance of X from the centre of mass is four
times the distance of star Y from the centre of mass. Again assuming the dimensions of the stars to be much
smaller than their separation
Orbital time period of star Y can be expressed as:

Options

A. `(2 pi R^(3//2))/(sqrt(5"GM"_("Y")))`
B. `(4 pi R^(3//2))/(sqrt("GM"_("Y")))`
C. `(2 pi R^(3//2))/(sqrt("5GM"_("x")))`
D. `(4 pi R^(3//2))/(sqrt("5GM"_("x")))`

Answer

C

Explanation

`(GM_(x)M_(y))/(R^(2))=(M_(y)V_(y)^(2) xx 5)/(R)`
Procedure as in Qn. No. 31