A planet has mass $\frac{1}{10}$ of that of earth, while radius is $\frac{1}{3}$ that of earth. If a person can throw a stone on earth surface to a height of $90 m$ , then he will be able to throw the stone on that planet to a height (in m)Assume that velocity of projection remains same on earth and planet.

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Solution

Maximum height reached on earth is $H_{e} = \frac{v^{2}}{2 g_{e}}$
$90 = \frac{v^{2}}{2 g_{e}}$
Maximum height reached on planet is
$H_{p} = \frac{v^{2}}{2 g_{p}}$
$\frac{90}{H_{p}} = \frac{g_{p}}{g_{e}}$ ..............(1)
Now acceleration due to gravity on earth is $g_{e} = \frac{G M_{e}}{(R_{e})^{2}}$ ,
acceleration due to gravity on planet is
$g_{p} = \frac{G M_{p}}{(R_{p})^{2}} = \frac{G \frac{M_{e}}{10}}{(\frac{R_{e}}{3})^{2}}$
$\frac{g_{p}}{g_{e}} = \frac{9}{10}$ ................(2)
From (1) and (2),
$H = 100 m$

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