Compute the additional velocity required by a satellite orbiting around earth with radius 2R to become free from earth's gravitational field. Mass of earth is M.

Options

A. `sqrt((2GM)/(R))(sqrt(2)-1)`
B. `sqrt((GM)/(2R))(sqrt(2)-1)`
C. `sqrt((GM)/(R))(sqrt(3)-1)`
D. `sqrt((GM)/(R))(sqrt(2)+1)`

Answer

A

Explanation

Required additional velocity,
`Delta v=v_(e)-v_(o)=sqrt(4gR)-sqrt(2gR)`
`=(2-sqrt(2))sqrt(gR)=(sqrt(2)-1)sqrt((2GM)/(R))`