A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is .........

Options

A. gx
B. `(gR)/(R-x)`
C. `(gR^2)/(R+x)`
D. `((gR^2)/(R+x))^(1/2)`

Answer

D

Explanation

`implies` For circular motion centripetal force = Gravitational force
`(mv_0^2)/(R+x) = (GMm)/((R+x)^2)`
`:. v_0 = sqrt((GM)/(R+x))= sqrt((rR^2)/(R+x))" " [ :. GM = gR^2]`
`:. v_0 = [(gR^2)/(R+x)]^(1/2)`