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 escape velocity of a body from this platform is $kv_e$, where v_e is its escape velocity from the surface of the earth. The value of k is :

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\(-\frac{GMm}{R+R} + \frac{1}{2}m(kv_e)^2 = 0 + 0\)

⇒ $kv_e$ = \(\sqrt{\frac{GM}{R}}\) and $v_e$ = \(\sqrt{\frac{2GM}{R}}\)

⇒ k = \(\frac{1}{\sqrt{2}}\)