Question

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 90m, then he will be able to throw the stone on that planet to a height

• A. 90 m
• B. 40 m
• C. 100 m
• D. 45 m

Answer 1

The correct option is C

100 m

Acceleration due to gravity $g=\frac{GM}{R^2}\therefore \frac{g_{planet}}{g_{earth}}=\frac{M_{planet}}{M_{earth}}{\left(\frac{R_{earth}}{R_{planet}}\right)}^2=\frac{1}{10}\times {\left(\frac{3}{1}\right)}^2=\frac{9}{10}$

If a stone is thrown with velocity u from the surface of the planet then maximum height

$H=\frac{u^2}{2g}\frac{H_{planet}}{H_{earth}}=\frac{g_{earth}}{g_{planet}}\Rightarrow H_{planet}=\frac{10}{9}\times H_{earth}=\frac{10}{9}\times 90=100metre$