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Question

The kinetic energy of a satellite in its orbit around the earth is $$E$$. What should be the minimum kinetic energy of the satellite so as to enable it to escape from the gravitational pull of the earth?


A
4E
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B
2E
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C
2E
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D
E
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Solution

The correct option is C $$\displaystyle 2 E$$
We know that $$\displaystyle v_e=\sqrt {2}v_0$$. where $$v_0$$ is orbital velocity.
$$K.E.$$ in the orbit, $$\displaystyle E=\frac {1}{2}M v_{0}^{2}$$
$$K.E.$$ to escape $$\displaystyle E=\frac {1}{2}M v_{e}^{2}= \frac {1}{2}M(2v_{0}^{2}) = \displaystyle \frac {1}{2}Mv_{0}^{2} \times 2=2E$$

Physics

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