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.
$$5\,{R_e}$$
Answer :
$$5\,{R_e}$$
Solution :
Range of projectile $$R = \frac{{{u^2}\sin 2\theta }}{g}$$
if $$u$$ and $$\theta $$ are constant then $$R \propto \frac{1}{g}$$
$$\eqalign{
& \frac{{{R_m}}}{{{R_e}}} = \frac{{{g_e}}}{{{g_m}}} \Rightarrow \frac{{{R_m}}}{{{R_e}}} = \frac{1}{{0.2}} \cr
& \Rightarrow {R_m} = \frac{{{R_e}}}{{0.2}} \Rightarrow {R_m} = 5{R_e} \cr} $$
Releted MCQ Question on Basic Physics >> Gravitation
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