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MHT CET 2021 (21 Sep, Shift 1) · Escape Velocity

Escape Velocity question from MHT CET 2021 (21 Sep, Shift 1)

Q50MHT CET 2021 · 21 SEP · SHIFT 1Medium

Escape Velocity

A particle of mass ' $m$ ' is kept at rest at a height $3R$ from the surface of earth, where ' $R$ ' is radius of earth and ' $M$ ' is the mass of earth. The minimum speed with which it should be projected, so that it does not return back is ( $g =$ acceleration due to gravity on the earth's surface)

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Answer: (a)

Height $3R$ means distance $r = 4R$ from the centre.
Escape speed there: $v = \sqrt{\frac{2GM}{r}} = \sqrt{\frac{2GM}{4R}}$ .
$v = \left[\frac{GM}{2R}\right]^{1/2}$ .
So the answer is (a).

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