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Question

# If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is : (Radius of earth =R)

A
2R
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B
R2
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C
R
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D
R4
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Solution

## The correct option is C RFor a satellite moving in circular orbit at a height h from Earth's surface, centripetal force is given by Fc=mv2Re+hThis force is provided by the Gravitational force of Earth, i.e.Fg=GMem(Re+h)2∴mv2Re+h=GMem(Re+h)2⇒v2=GMeRe+h⇒v=√GMeRe+hEscape velocity is given by,ve=√2GMeReIt is given that the speed of the satellite is half of the escape speed.∴[12(√2GMeRe)]2=GMeRe+h⇒GMe2Re=GMeRe+h⇒2Re=Re+h⇒h=Re

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