A satellite of mass m revolves around the earth of radius R at a hight 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. `(gR^2)/(R+x)`
B. `(gR)/(R -x)`
C. gx
D. `((gR^2)/(R +x))^(1//2)`

Answer

D

Explanation

(d) Gravitational force provides the necessary centripetal
force.
`(mv^2)/((R+x)) = (GmM)/((R + x)^2) also g = (GM)/(R^2)`
`:.v^2 = (gR^2)/(R +x) rArr v = ((gR^2)/(R + x))^(1//2)`