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}}] $
Show Answer
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}}}] $
