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(D) The formula for the horizontal range of a projectile is given by $R = \frac{u^2 \sin 2	heta}{g}$.Given that the velocity of projection $u$ and th

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$5$

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(D) The formula for the horizontal range of a projectile is given by $R = \frac{u^2 \sin 2	heta}{g}$.Given that the velocity of projection $u$ and the angle of projection $	heta$ are constant,the range $R$ is inversely proportional to the acceleration due to gravity $g$,i.e.,$R \propto \frac{1}{g}$.Let $R_e$ and $g_e$ be the range and acceleration due to gravity on Earth,and $R_m$ and $g_m$ be the range and acceleration due to gravity on the Moon.We are given $g_m = 0.2 \, g_e$.Using the proportionality $R_m \, g_m = R_e \, g_e$,we get:$R_m = R_e \left( \frac{g_e}{g_m} ight)$$R_m = R_e \left( \frac{g_e}{0.2 \, g_e} ight)$$R_m = \frac{R_e}{0.2} = 5 \, R_e$.Therefore,the maximum range on the surface of the moon is $5 \, R_e$.

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