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Question

# An artificial satellite is moving around earth in a circular orbit with speed equal to one fourth the escape speed of a body from the surface of earth. The height of satellite above earth is : (R is radius of earth)

A
3R
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B
5R
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C
7R
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D
8R
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Solution

## The correct option is D 8RLet's consider,r= height of the satellite above the earthR= radius of the earthG= gravitational constantg= acceleration due to gravityThe escape velocity of a body from the surface of earth,ve=√2GMR14.ve=14√2GMR. . . . . .(1)The orbital velocity of the satellite is given byvo=√GMr. . . . . .(2)Equation equation (1) and (2), we get√GMr=14√2GMRGMr=116.2GMRr=8RThe correct option is D.

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