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Question

A body is projected vertically upwards from the surface of earth with a velocity equal to half the escape velocity. If R is the radius of the earth, maximum height attained by the body from the surface of earth is

A
R6
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B
R3
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C
2R3
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D
R4
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Solution

The correct option is B R3
Let H be the maximum height.
By conservation of energy,
T.Ei=T.EfK.Ei+P.Ei=P.Ef12mVe24+(GMmR)=GMmR+Hm82GMRGMmR=GMmR+H (V2e=2GMR) 3GMm4R=GMmR+HR+H=4R3H=R3

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