The Earth is assumed to be a sphere of radius R. A platform

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The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the Earth. The velocity of a body from this platform is f v, where v is its velocity from the surface of the Earth. The value of f is

Potential energy at height R = -	G M m
	2R

If m be the mass of a body which is thrown with velocity v_e so that it goes out of gravitational field from distance R, then

	1	mv_e² =	GM	.m
	2		2R

or v_e = √2 gR , So , v = √2 v_e

or , v_e =	v
	√2

Comparing it with given equation, f =	1
	√2