Question

A fully dressed astronaut can jump to a maximum height 50 cm on the surface of earth. If average density of moon is $\frac{2}{3}$ that of the earth and radius of moon is $\frac{1}{4}$ that of earth, maximum height through which the astronaut can jump on the surface of moon is-

Answer 1

$g=\frac{GM}{R^2}=\frac{G\frac{4}{3}\pi R^3\rho }{R^2}=\frac{4}{3}G\pi \rho R$

$\frac{g_m}{g_e}=\frac{{\rho }_m{R}_m}{{\rho }_e{R}_e}=\frac{2}{3}.\frac{1}{4}=\frac{1}{6}$

And, $h=\frac{v^2}{2g}$

Hence, $\frac{h_m}{h_e}=\frac{g_e}{g_m}$

$⟹h_m=6\times 50cm=300cm=3m$