A particle of mass m is thrown upwards from the surface of the earth, with a vilocity U. The mass and the radius of the earth are respectively, M and G is gravitational constant and g is acceleration due to gravity on the surface of the 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((GM)/R)`

Answer

A

Explanation

`implies` Here u becomes a escape velocity
i.e. u `= sqrt (2gR) ` but `g = (GM)/R^2`
`:. U = sqrt(2(GM)/R^2.R)`
`= sqrt((2GM)/R)`