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

Answer

B

Explanation

According to law of conservation of mechanical energy
` 1/2 mu^2 - (GMm)/( R) = 0 " or " u^2 = (2GM)/( R) " or " u = sqrt(2gR) ( because g = (GM)/(R^2))`