Question

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 geostationary satellite will be

• A. $\frac{R^{2}g}{\omega }$
• B. $\frac{R^2{\omega }^2}{g}$
• C. $\frac{Rg}{{\omega }^2}$
• D. $\frac{R^{2}g}{{\omega }^2}$

Answer 1

The correct option is D $\frac{R^{2}g}{{\omega }^2}$

$Orbitalvelocity{v}_0=\sqrt{\frac{GM}{r}}=\sqrt{\frac{g{R}^2}{r}}and{v}_0=r\omega Thisgives{r}^3=\frac{R^{2}g}{{\omega }^2}$