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Question

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 mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)

A
(GMR)
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B
(GM2R)
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C
(2GMR)
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D
(GM3R)
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Solution

The correct option is B (GM2R)

As we know, the minimum speed with which a body is projected so that it does not return back is called escape speed, which is given byve=2GMrWhere r is the distance from the centre of the earth,
given, r=R+3R=4R

ve=2GM4R

ve=GM2R

Hence, option (b) is the correct answer.
Why this question:

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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