Question

If the mean radius of eaith is R, its angular velocity is $\omega$ and the, acceleration due to gravity at the surface of the earth is 'g' thien the, cube of the radius of the orbit of a satellite will be

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

Answer 1

Answer: (C)

Time period of satellite,
$T=\frac{2 \pi r^{3 / 2}}{\sqrt{G M}}$ or $\sqrt{G M}=\frac{2 \pi}{T} \cdot r^{3 / 2}$
$
\frac{2 \pi}{T}=\omega
$
$\therefore \omega r^{3 / 2}=\sqrt{G M}$ or $r^{3}=\frac{G M}{\omega^{2}}=\frac{g R^{2}}{\omega^{2}}$