Physics - Gravitation Question with Solution | TestHub

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

For the planet,${\mathrm{g}}_1=\frac{{\mathrm{GM}}_1}{{\mathrm{R}}_1^2}=\frac{4}{3}\mathrm{ }{\mathrm{\pi R}}_1\mathrm{\rho G}$

$\frac{\mathrm{g}}{{\mathrm{g}}_1}=\frac{\mathrm{R}}{{\mathrm{R}}_1}=\frac{6400}{320}=20$

Let$\mathrm{h}$and${\mathrm{h}}_1$be the distance up to which the man can jump on the surface of the earth and planet, then

$\mathrm{mgh}={\mathrm{mg}}_1{\mathrm{h}}_1$

$\therefore \mathrm{ }{\mathrm{h}}_1=\frac{\mathrm{g}}{{\mathrm{g}}_1}\mathrm{ }\mathrm{h}=20\times 5=100\mathrm{ }\mathrm{m}$