The mean radius of the earth is R, its angular speed about its own axis $\omega$ and the acceleration due to gravity at the earth surface is g. The cube of radius of orbit of 'geostationary satellite' will be:
Answer & explanation
Correct answer: option 4
$mr \omega^2=\frac{GMm}{r^2} \Rightarrow r \omega^2=\frac{GM}{r^2}$
$\Rightarrow r^3=\frac{GMm}{\omega^2}=\frac{GM}{R^2} . \frac{R^2}{\omega^2}$
$\Rightarrow r^3=g \frac{R^2}{\omega^2}$