Question

A satellite moves around the earth in a circular orbit with 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. $-\frac{3}{2}m{v}^2$
• D. $-\frac{1}{4}m{v}^2$

Answer 1

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

$T.E=K.E+P.E=\frac{1}{2}m{v}^2+(-\frac{GMm}{r})$

Now as $F_{centrifugal}=F_{gravitational}⟹\frac{m{v}^2}{r}=\frac{GMm}{r^2}$

Thus, $\frac{GMm}{r}=m{v}^2$

Now, $T.E=\frac{1}{2}m{v}^2-m{v}^2=-\frac{1}{2}m{v}^2$