Question

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

Answer 1

Acceleration due to gravity is given by,

$g=\frac{GM}{R^2}$

$\therefore \frac{g_{\text{planet}}}{g_{\text{earth}}}=\frac{M_{\text{planet}}}{M_{\text{earth}}}{\left(\frac{R_{\text{earth}}}{R_{\text{planet}}}\right)}^2$

$\frac{1}{10}\times {\left(\frac{3}{1}\right)}^2=\frac{9}{10}$

If stone is thrown with velocity $u$ from the surface of the planet, then maximum height achieved by it is,

$H=\frac{u^2}{2g}$

$\frac{H_{\text{planet}}}{H_{\text{earth}}}=\frac{g_{\text{earth}}}{g_{\text{planet}}}$

$\Rightarrow H_{\text{planet}}=\frac{10}{9}\times H_{\text{earth}}$

$=\frac{10}{9}\times 90=100\text{metre}$.