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........

A particle of mass m is thrown upwards from the surface of the earth,

1.	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........
Answer» `sqrt((2GM)/R)` `sqrt((2GM)/R^2)` `sqrt(2gR^2)` `sqrt((GM)/R)` Solution :`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)`