A binary star has stars of masses m and nm (where n is a numerical factor) having seperation of their centres as
r If these stars revolve because of gravitational force of each other, the period of revolution is given by

Options

A. `(2 pi r^(3//2))/((("Gnm"^(2))/(m(1+n)))^(1/2))`
B. `(2pi r^(1//2))/((("Gm"(1+n))/("nm"^(2)))^(1/2))`
C. `(2pir^(3_(1)))/(2/3"Gnm")`
D. `(2pir^(3//2))/((3/2"GMn")^(1/2))`

Answer

A

Explanation

Here reduced mass = `(m xx nm)/(m+nm)=(nm^(2))/(m(1+n))`
`implies T= 2 pi sqrt((r)/(g)),[(g=(GM))/(r^(2))]` `therefore T=(2 pi r^(3//2))/(sqrt((Gnm^(2))/(m(1+n))))`