Q. A satellite is revolving around the earth with a kinetic energy E . The minimum addition of kinetic energy needed to make it escape from its orbit is
A) $2E$
B) $\sqrt{E}$
C) $E/2$
D) $E$
Explanation
(d) Kinetic energy of satellite in its orbit
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E = \frac{1}{2}{mv}_{o}^{2}$
$or\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E = \frac{1}{2}m\left( \frac{GM}{r} \right) = \frac{GMm}{2r}$
kinetic energy at escape velocity
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E^{'} = \frac{1}{2}{mv}_{e}^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{2}m\left( \frac{2GM}{r} \right) = \frac{GMm}{r}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2E$
Therefore, additional kinetic energy required
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2E - E = E$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.