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

Answer

D

Explanation

For the satellite the gravitational force provides the necessary centripetal force i.e.,
`(GM_(e)m)/((R+x)^(2))=(mv_(2)^(2))/((R+x))` or `(GM_(e))/(R^(2))=g`
`v_(0)=sqrt((gR^(2))/(R+x))`