A test particle is moving in a circular orbit in the gravitational field produced by a mass density `rho(r)=K/(r^(2))`. Indentify the correct relation between the radius R of the particle's orbit and its period T :

Options

A. T/R is constant
B. TR is a constant
C. `T^2//R^3`is a constant
D. `T//R^2` is a constant

Answer

A

Explanation

`rho(r)=K/r^2, (Mv^2)/R = (GM')/R^2 " " (Mv^2)/R=(G int_0^R rho(r)4pir^2dn)/R^2 , m((2pi)/T)^2 R=(GK4piR)/R^2 " " T/R`= constant