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NEET 2006 (AIPMT) · Escape Velocity

Escape Velocity question from NEET 2006 (AIPMT)

Q76NEET 2006 · AIPMTMedium

Escape Velocity

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 fv, where v is its escape velocity from the surface of the Earth. The value of f is

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Answer: (c)

Escape speed at distance $r$ : $\sqrt{\frac{2GM}{r}}$ ; platform is at $r = 2R$ .
$v' = \sqrt{\frac{2GM}{2R}} = \frac{v}{\sqrt{2}}$ .
So the answer is (c) $f = 1/\sqrt{2}$ .

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