The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

One

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Two

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Half

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Infinity

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Solution

The correct option is B
Two

K.E. required for satellite to escape from earth's gravitational field $\frac{1}{2} m v_{e}^{2} = \frac{1}{2} m (\sqrt{\frac{2 G M}{R}})^{2} = \frac{G M m}{R}$
K.E. required for satellite to move in circular orbit
$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m (\sqrt{\frac{G M}{R}})^{2} = \frac{G M m}{2 R}$
The ratio between these two energies=2

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The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

The correct option is B Two K.E. required for satellite to escape from earth's gravitational field 12mv2e=12m(√2GMR)2=GMmR K.E. required for satellite to move in circular orbit 12mv20=12m(√GMR)2=GMm2R The ratio between these two energies=2