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

Answer: (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 $=KE+PE$

$=\frac{1}{2}m{v}^2-m{v}^2=-\frac{1}{2}m{v}^2$