The mean radius of the earth is `R`, its angular speed on its own axis is `omega` and the acceleration due to gravity at earth's surface is `g`. The cube of the radius of the orbit of a geo-stationary satellite will be

Options

A. `R^2g//omega`
B. `R^2omega^2//g`
C. `Rg//omega^2`
D. `R^2g//omega^2`

Answer

D

Explanation

`v_0=sqrt((GM)/r)`
`rArrv_0=sqrt((gR^2)/r)rArr(romega)^2=(gR^2)/rrArrr^3=(gR^2)/(omega^2)`