Question

A potential energy of satellite, having mass $m$ and rotating at height of $6.4\times 10^{6}m$ from the earth surface will be :

• A. $-0.5mg{R}_e$
• B. $-1.5mg{R}_e$
• C. $0.67mg{R}_e$
• D. none of these

Answer 1

Answer: (A)

Here : Mass of the satellite $=m$
Height of the satellite from the earth
$h=6.4\times 10^{6}m$
Gravitation potential energy of the satellite at a height $h$ is given by,
$U=-\frac{G{M}_{e}m}{R_e+h}=-\frac{g{R}_e^{2}m}{2R_e}$
$=-\frac{g{R}_{e}m}{2}=-0.5mg{R}_e$
(where $G{M}_e=g{R}_e^2$ and $h=R_e$ )