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A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

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R/3

R/2

R/4

R/5

answer is A.

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Detailed Solution

If body is projected with velocity v $(v < v_{e})$ then
height up to which it will rise, $h = \frac{R}{\frac{v_{e}^{2}}{v^{2}} - 1}$

$v = \frac{v_{e}}{2} (given) ∴ h = \frac{R}{{(\frac{v_{e}}{v_{e} / 2})}^{2} - 1} = \frac{R}{4 - 1} = \frac{R}{3}$

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