A spaceship is launched in to a circular orbit of radius `R` close to surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is (`g`=acceleration due to gravity)

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))`