A spaceship is launched into a circular orbit close to earth's surface. The additional velocity that should be imparted to the spaceship in the orbit to overcome the gravitational pull is
(Radius of earth 6400 km and `g = 9.8 m s^(-2)`)

Explanation

let `DeltaK` be the additional kinetic energy imparted to the spaceship to overcome the gravitation pull then
`K=(GMm)/(2R)` Total kinetic energy `=(GMm)/(2R)+DeltaK=(GMm)/(2R)+(GMm)/(2R)=(GMm)/(R)`
then `(1)/(2)mv_(2)^(2)=(GMm)/(R)impliesv_(2)=sqrt((2GM)/(R))` but `v_(1)=sqrt((GM)/(R))`
So additional velocity `=v_(2)-v_(1)=sqrt((2GM)/(R))-sqrt((GM)/(R))=(sqrt(2)-1)sqrt((GM)/(R))`