The mean radius of the earth is R, its angular speed on its own axis is ω

Question

The mean radius of the earth is R, its angular speed on its own axis is

ω

and the acceleration due to gravity at earth's surface is g. The cube of the radius of the orbit of a geostationary satellite will be

Options:

A . R2gω

B . R2ω2g

C . Rgω2

D . R2gω2

Answer: Option D
:
D

O r b i t a l v e l o c i t y v_{0} = \sqrt{\frac{G M}{r}} = \sqrt{\frac{g R^{2}}{r}} a n d v_{0} = r ω T h i s g i v e s r^{3} = \frac{R^{2} g}{ω^{2}}

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