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

Answer

D

Explanation

`mromega^(2)=(GMm)/(r^(2))`
`impliesromega^(2)=(GM)/(r^(2))`
`impliesr^(3)=(GM)/(omega^(2))=(GM)/(R^(2)).(R^(2))/(omega^(2))`
`impliesr^(3)=g(R^(2))/(omega^(2))`