If T is the period of a satellite revolving very close to the surface of the earth and if `rho` is the density of the earth, then

Options

A. `T prop rho`
B. `T prop (1)/(rho)`
C. `T prop sqrt(rho)`
D. `T prop (1)/(sqrt(rho))`

Answer

D

Explanation

Use `T = 2pi sqrt((R^(3))/(GM)) " " therefore T prop sqrt((R^(3))/((4)/(3)pi R^(3)rho))`
`therefore T prop (1)/(sqrt(rho))`