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 above surface is R/n. The value of n is

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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 above surface is $R / n .$ The value of n is

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Detailed Solution

If body is projected with velocity $V (v < v_{e})$ then height up to which it will rise, $h = \frac{R}{\frac{v_{e}^{2}}{v^{2}} - 1}$
$v = \frac{v_{e}}{2} (g i v e n) ∴ h = \frac{R}{{(\frac{v_{e}}{v_{e} / 2})}^{2} - 1} = \frac{R}{4 - 1} = \frac{R}{3}$