A spaceship is launched into a circular orbit close to earth's surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull? (Take, radius of earth = 6400kmand g = 9.8 ms-2)[AIIMS 2017]

The orbital velocity of spaceship in circular orbit, vo = GMrIf spaceship is very close to earth surface, then r = radius of earth (R).∴  vo=GMR=R2gR=Rg   Since, g=GMR2Here,  R=6400 km=6.4×106 m and g=9.8 ms-2∴  vo=6.4×106×9.8= 7.92×103 m/s = 3.28 km s-1∴  Additional velocity required= 11.20 - 7.92 = 3.28 km s-1Therefore, velocity of 3.28 km s-1 must be added to orbital velocity of spaceship to overcome the gravitational pull.