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)

100m

Answer 2

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

∴$\frac{g_{planet}}{g_{earth}} = \frac{M_{planet}}{M_{earth}}\left( \frac{R_{earth}}{R_{planet}} \right)^{2} = \frac{1}{10} \times \left( \frac{3}{1} \right)^{2} = \frac{9}{10}$

If a stone is thrown with velocity $u$ from the surface of the planet then maximum height $H = \frac{u^{2}}{2g}$

$\frac{H_{planet}}{H_{earth}} = \frac{g_{earth}}{g_{planet}}$⇒$H_{planet} = \frac{10}{9} \times H_{earth} = \frac{10}{9} \times 90$ = 100 metre.