Question

A geostationary satellite is orbiting the earth at a height $6R$ above the surface of the earth, where $R$ is the radius of earth. The time period of another satellite revolving around earth at a height $2.5R$ from earth's surface is :

• A. $12\sqrt{2}$ hr
• B. $12$ hr
• C. $6\sqrt{2}$ hr
• D. $6$ hr

Answer 1

The correct option is C $6\sqrt{2}$ hr

Time period is related to orbit radius as
$T^2\propto R^3$
$\Rightarrow \frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^3}$
Given $R_1=7R$ and $R_2=3.5R$
$\Rightarrow \frac{T_1^2}{T_2^2}={\left(\frac{7R}{3.5R}\right)}^3=8$
$\Rightarrow T_2=\frac{T_1}{\sqrt{8}}=\frac{24}{2\sqrt{2}}=6\sqrt{2}$ hours
Option C.