Physics - Gravitation Question with Solution | TestHub

For a geostationary satellite, the angular velocity is the same as the angular velocity of the earth, $\omega$.

The gravitational force provides the necessary centripetal force:

$\frac{GMm}{r^2}=m{\omega }^{2}r$

$r^3=\frac{GM}{{\omega }^2}$

Acceleration due to gravity at the surface of the earth is given by:

$g=\frac{GM}{R^2}\Rightarrow GM=g{R}^2$

Substituting the value of $GM$ in the expression for $r^3$:

$r^3=\frac{R^{2}g}{{\omega }^2}$

Answer: $\frac{R^{2}g}{{\omega }^2}$