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Acceleration Due to Gravity

A satellite i...

Question

A satellite in a circular orbit about the earth has a kinetic energy $E_{K}$ . What is the minimum amount of energy to be added so that it escape from the earth?

A

2 E_{K}

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B

\frac{E_{K}}{4}

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C

\frac{E_{K}}{2}

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D

E_{K}

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Solution

The correct option is D $E_{K}$
Total energy $= - \frac{G M m}{2 r}$
Kinetic energy $= \frac{G M m}{2 r}$
To escape, energy needed

$= - T E = \frac{G M m}{2 r} =$ Kinetic energy $E_{K}$ .

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