A) \[\sqrt{2}E\]
B) 2 E
C) \[E/\sqrt{2}\]
D) E
E) \[\frac{E}{2}\]
Correct Answer: B
Solution :
When a satellite is orbitting close to earth, its orbital velocity, \[{{v}_{o}}=\sqrt{\frac{GM}{R}}\] escape velocity, \[{{v}_{e}}=\sqrt{\frac{2GM}{R}}\] Here, kinetic energy, \[E=\frac{1}{2}mv_{o}^{2}=\frac{1}{2}m\frac{GM}{R}\] KE required to escape, \[{{E}_{1}}=\frac{1}{2}mv_{e}^{2}=\frac{1}{2}m\left( \frac{2GM}{R} \right)=2E\] \[\therefore \] Additional KE required\[=2E-E=E\]
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