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

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 $(v)$