Q. Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If $R_{e}$ is the maximum range of a projectile on the earth’s surface, what is the maximum range on the surface of the moon for the same velocity of projection
A) $0.2\ R_{e}$
B) $2\ R_{e}$
C) $0.5\ R_{e}$
D) $5\ R_{e}$
Explanation
(d) Range of projectile $R = \frac{u^{2}\sin{2\theta}}{g}$
If $u$ and $\theta$ are constant then $R \propto \frac{1}{g}$
$\frac{R_{m}}{R_{e}} = \frac{g_{e}}{g_{m}} \Rightarrow \frac{R_{m}}{R_{e}} = \frac{1}{0.2} \Rightarrow R_{m} = \frac{R_{e}}{0.2} \Rightarrow R_{m} = 5R_{e}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.