A particle of mass `m` is thrown upwards from the surface of the earth, with a velocity `u`. The mass and the radius of the earth are, respectively, `M` and `R`. `G` is gravitational constant `g` is acceleration due to gravity on the surface of earth. The minimum value of `u` so that the particle does not return back to earth is

Options

A. `sqrt((2GM)/R)`
B. `sqrt((2GM)/(R^(2))`
C. `sqrt(2gR^(2))`
D. `sqrt((4GM)/(R^(2))`

Answer

A

Explanation

Escape velocity
`v_(e)=sqrt(2gR)`
`v_(e)=sqrt((2GM)/(R^(2))R) ( :' GM=gR^(2))`
`v_(e)=sqrt((2GM)/R)`