Question

A satellite of mass $m$, is orbiting around the earth at a distance $r$ from centre of earth, if it stopped suddenly the loss in total energy will be

• A. $\frac{GMm}{2r}$
• B. $-\frac{GMm}{r}$
• C. $-\frac{GMm}{2r}$
• D. none of these

Answer 1

Answer: (A)

$\frac{GMm}{2r}$

Initial energy of satellite $E_1=-\frac{GMm}{r}+\frac{1}{2}m{v}^2$

When it stopped, $E_2=-\frac{GMm}{r}$

Loss in total energy is $E_2-E_1=\frac{1}{2}m{v}^2$

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

$v^2=\frac{GM}{r}$

$=\frac{GMm}{2r}$