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  • The mean radius of the earth is , its angular speed about its own axis <img alt="\omega" src="http

The mean radius of the earth is \mathrm{ R}, its angular speed about its own axis \omega and the acceleration due to gravity at the earth surface is \mathrm{ g}. The cube of radius of orbit of 'geostationary satellite' will be:
 

Option: 1

\mathrm{\left(R^2 g / \omega\right)}

 


Option: 2

\mathrm{\quad\left(R^2 \omega / g\right)}
 


Option: 3

\mathrm{\left(\mathrm{Rg} / \omega^2\right)}
 


Option: 4

\mathrm{\quad\left(R^2 g / \omega^2\right)}


Answers (1)

best_answer

\mathrm{ m r \omega^2=\frac{G M m}{r^2} \Rightarrow r \omega^2=\frac{G M}{r^2} }

\mathrm{ \Rightarrow r^3=\frac{G M m}{\omega^2}=\frac{G M}{R^2} \cdot \frac{R^2}{\omega^2} }

\mathrm{ \Rightarrow r^3=g \frac{R^2}{\omega^2} . }

Hence option 4 is correct.


 

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mansi

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