A particle of masses 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 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) √( 2GM / R)
(b) √( 2GM / R)²
(c) √( 2G R²)
(d) √( 2GM / R)²

Correct Answer:

√( 2GM / R)

Explanation:

The velocity u should be equal to the escape velocity. That is, u = √(2gR)
But g = GM / R² ⇒ u = √(2 . GM / R² . R)
√( 2GM / R)