Question

A satellite is in a circular orbit around the earth at an altitude $R$ above the earth's surface, where $R$ is the radius of the earth. If $g$ is the acceleration due to gravity on the surface of the earth, the speed of the satellite is:

• A. $\sqrt{2Rg}$
• B. $\sqrt{Rg}$
• C. $\sqrt{\frac{Rg}{2}}$
• D. $\frac{\sqrt{Rg}}{4}$

Answer 1

The correct option is C $\sqrt{\frac{Rg}{2}}$

The gravitational force acting on satellite at an altitude $R$ causes the centripetal acceleration it required.

Thus, $\frac{GMm}{(2R{)}^2}=\frac{m{v}^2}{2R}$

$⟹v=\sqrt{\frac{GM}{2R}}$

Gravitational acceleration $g=\frac{GM}{R^2}$

$⟹v=\sqrt{\frac{Rg}{2}}$