First slide

Universal law of gravitation

Question

The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth’s surface is g. What will be the radius of the orbit of a geostationary satellite ?

Easy

A

$\large \left ( \frac {R^2g}{\omega^2} \right )^{1/3}$
B

$\large \left ( \frac {Rg}{\omega^2} \right )^{1/3}$
C

$\large \left ( \frac {R^2\omega^2}{g} \right )^{1/3}$
D

${({R^{^2}}g/\omega )^{1/3}}$

Solution

Gravitational force = Centripetal force
$\large \frac{{GMm}}{{{r^2}}} = m\,r\,{\omega ^2}$
$\large \frac{{GM}}{{{r^3}}} = \,{\omega ^2}but\;g = \frac{{GM}}{{{R^2}}} \Rightarrow GM = g{R^2}$
$\large \therefore {r^3} = \frac{{GM}}{{{\omega ^2}}} = \frac{{g{R^2}}}{{{\omega ^2}}} \Rightarrow r = {\left( {\frac{{g{R^2}}}{{{\omega ^2}}}} \right)^{\frac{1}{3}}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App