The mean radius of the earth is R, its angular speed on its own a… - Vidyadip

MCQ

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
${R^2}g/\omega $
B
${R^2}{\omega ^2}/g$
C
$Rg/{\omega ^2}$
✓
${R^2}g/{\omega ^2}$

✓

Answer

Correct option: D.

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

d
(d) Orbital velocity ${v_0} = \sqrt {\frac{{GM}}{r}} = \sqrt {\frac{{g{R^2}}}{r}} $ and ${v_0} = r\omega $
This gives ${r^3} = \frac{{{R^2}g}}{{{\omega ^2}}}$

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