An artificial satellite is moving in a circular orbit around the earth at a height fi from the surface of the earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely on the earth, the speed with which it will hit the surface of the earth will be

When the satellite is stopped, its kinetic energy is zero and total energy is only potential energy. This is given byE1=−GMmr=−GmM2R (r=R+R)Potential energy of the satellite on the earthE2=−GmMRloss of potential energy=E1−E2=−GmM2R−−GmMR=GmM2RThis is converted into kinetic energy. Hence12mv2=GMm2Ror v2=GMR=gRor v=(gR)