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NEET 2011 (AIPMT, Mains) · Escape Velocity

Escape Velocity question from NEET 2011 (AIPMT, Mains)

Q74NEET 2011 · AIPMT · MAINSEasy

Escape Velocity

A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. 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

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Answer: (b)

Not returning means $u \ge$ escape speed: $\frac{1}{2}mu^2 = \frac{GMm}{R}$
$u_{min} = \sqrt{\frac{2GM}{R}}$
So the answer is (b).

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