Question

The total energy of an artificial satellite of mass $m$ revolving in a circular orbit around the earth with a speed $v$ is

• A. $\frac{1}{2} mv^2$
• B. $\frac{1}{4} mv^2$
• C. $ -\frac{1}{4} mv^2$
• D. $ - mv^2$
• E. $ - \frac{1}{2} mv^2$

Answer 1

Answer: (E)

$\because$ Total energy of the satellite is
$E=-\frac{1}{2} \frac{G M_{e} \,m}{R_{e}}$
where$K=\frac{1}{2} \frac{G M_{e} \,m}{R_{e}}$
$\therefore $ Total energy $=-$ Kinetic energy
$E=-\frac{1}{2} m v^{2}$
Putting the value of $KE$ in the form of mass of a satellite $(m)$ and speed $(v)$