Question

If $R$ is the average radius of earth, $\omega$ is its angular velocity about its axis and $g$ is the gravitational acceleration on the surface of earth then the cube of the radius of orbit of a geostationary satellite will be equal to.

• 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

Answer: (D)

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

As, $mr{\omega }^2=\frac{GMm}{r^2}$

$⟹r{\omega }^2=\frac{GM}{r^2}$

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