Question

An artificial satellite revolves around the earth in a circular orbit with a speed $v$. If $m$ is the mass of the satellite, its total energy is.

• A. $\frac{1}{2}m{v}^2$
• B. $-\frac{1}{2}m{v}^2$
• C. $-m{v}^2$
• D. $\frac{3}{2}m{v}^2$

Answer 1

The correct option is B $-\frac{1}{2}m{v}^2$

Kinetic energy of satellite, $KE=\frac{1}{2}m{v}^2$
where $v=\sqrt{\frac{GM}{r}}$
Potential energy of satellite, $PE=\frac{-GMm}{r}=-m{v}^2$
$\therefore$ Total energy $=KE+PE$
$=\frac{1}{2}m{v}^2-m{v}^2$
$=-\frac{1}{2}m{v}^2$