Question

A man can jump $1.5$m high on the earth. Calculate the approximate height he might be able to jump on a planet whose density is one-quarter that of the earth and whose radius is one-third of the earth's radius.

Answer 1

The work done that man did for jumping $1.5m$ height in earth.

$⟹mgh=mg\times 1.5$

$D_E\to$ Density of earth, $R_E\to$ Radius of earth, in second planet.

$D_p=\frac{D}{4},R_p=\frac{R}{3}$

Volume $V_p=\frac{4}{3}\pi \times \frac{R^3}{27}$

$D_p=\frac{M_p}{v_p}$

$M_p=D_p\times v_p=\frac{D_E}{4}\times \frac{v_E}{27}=\frac{M_e}{108}$

$g=\frac{GM}{R^2}=\frac{G\times M_{\times }9}{108\times R^2}$

$⟹\frac{G{M}_E}{12R^2}=\frac{g}{12}$

$mg\times 1.5=m\times \frac{g}{12}\times h$

$h=12\times 1.5=18m$