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

• A. $R ^ { 2 } g / \omega$
• B. $R ^ { 2 } \omega ^ { 2 } / g$
• C. $R g / \omega ^ { 2 }$
• D. $R ^ { 2 } g / \omega ^ { 2 }$

Answer 1

Answer: (D)

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

Answer 2

Orbital velocity $v _ { 0 } = \sqrt { \frac { G M } { r } } = \sqrt { \frac { g R ^ { 2 } } { r } }$ and

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