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Question

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 the earth is

A
2gR2
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B
2GMR2
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C
2GMR
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D
2gMR2
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Solution

The correct option is C 2GMR
Particle will not return if it is thrown upwards with escape velocity.

Conserving mechanical energy between the instants the particle is at the surface of the earth and at a very large distance

Ui+Ki=Uf+Kf

At a very large distance, Uf=0 and for the particle to just escape gravity. its final velocity will be 0, so Kf=0.

GMmR+12mv2e=0+0

ve=2GMR

Hence, option (c) is correct.

Why this question ?Tip: Escape velocity can be calculated for any orbit not just the surface of the planet. For a particle to escape, its total mechanical energy should be equal to zero.

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