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 $90\, m$, 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

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