Question

A planet has mass $1/10$ of that of earth, while radius is $1/3$ 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. $90m$
• B. $40m$
• C. $100m$
• D. $45m$

Answer 1

Answer: (C)

Acceleration due to gravity $g=\frac{GM}{R^2}$

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

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

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

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

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

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

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