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Question: An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the eart...

An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

A

gR2R+h\frac { g R ^ { 2 } } { R + h }

B

gR

C

gRR+h\frac { g R } { R + h }

D

gR2R+h\sqrt { \frac { g R ^ { 2 } } { R + h } }

Answer

gR2R+h\sqrt { \frac { g R ^ { 2 } } { R + h } }

Explanation

Solution

v0=GMr=gR2R+hv _ { 0 } = \sqrt { \frac { G M } { r } } = \sqrt { \frac { g R ^ { 2 } } { R + h } }