Gravitation Question 251

Question: 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[CBSE PMT 1992]

Options:

A) $ [R^{2}g/\omega ] $

B) $ [R^{2}{{\omega }^{2}}/g] $

C) $ [Rg/{{\omega }^{2}}] $

D) $ [R^{2}g/{{\omega }^{2}}] $

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Answer:

Correct Answer: D

Solution:

Orbital velocity $ [v_{0}=\sqrt{\frac{GM}{r}}=\sqrt{\frac{gR^{2}}{r}}] $

and $ [v_{0}=r\omega ] $

This gives $ [r^{3}=\frac{R^{2}g}{{{\omega }^{2}}}] $



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