Question

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 earths 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. Zero
• E. $ 5{{R}_{e}} $

Answer 1

Answer: (E)

Maximum range
$ {{R}_{\max }}=\frac{{{u}^{2}}}{g}\Rightarrow {{R}_{\max }}\propto \frac{1}{g} $
$ \therefore $ $ \frac{R{{}_{\max }}}{{{R}_{\max }}}=\frac{{{g}_{e}}}{{{g}_{m}}}=\frac{{{g}_{e}}}{0.2\,{{g}_{e}}} $
$ \Rightarrow $ $ R_{\max }^{}=5{{R}_{e}} $