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. $ -0.5\,mgR_{e}$
• B. $ -1.5\,mgR_{e}$
• C. $ 0.67\,mgR_{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,
$U=-\frac{G M_{e} m}{R_{e}+h}=-\frac{g R_{e}^{2} m}{2 R_{e}}$
$=-\frac{g R_{e} m}{2}=-0.5\, m g R_{e}$
(where $G M_{e}=g R_{e}^{2}$ and $h=R_{e}$ )