What is the periodic times of a satellite revolving very close to the surface of the earth, of density `rho` ?

Options

A. `sqrt((3pi)/(rho G))`
B. `sqrt((5pi)/(rho G))`
C. `sqrt((2pi)/(rho G))`
D. `sqrt((4pi)/(rho G))`

Answer

A

Explanation

`T=2pi sqrt((R^(3))/(GM)) = 2pi sqrt((R^(3))/(G.(4)/(3)pi R^(3)xx rho))=2pi sqrt((3)/(4pi G rho))`
`therefore T = sqrt((4pi^(2).3)/(4pi G rho))=sqrt((3pi)/(rho G))`