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(D) The acceleration due to gravity $g$ on the surface of a planet is given by $g = \frac{GM}{R^2}$.Since mass $M = 	ext{Volume} 	imes 	ext{Density

Vedclass · Accepted Answer

$g_1:g_2 = R_1 \rho_1 : R_2 \rho_2$

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(D) The acceleration due to gravity $g$ on the surface of a planet is given by $g = \frac{GM}{R^2}$.Since mass $M = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi R^3 ho$,we substitute this into the formula:$g = \frac{G (\frac{4}{3} \pi R^3 ho)}{R^2} = \frac{4}{3} \pi G R ho$.Thus,$g \propto R ho$.Therefore,the ratio of the acceleration due to gravity for two planets is $\frac{g_1}{g_2} = \frac{R_1 ho_1}{R_2 ho_2}$,which can be written as $g_1 : g_2 = R_1 ho_1 : R_2 ho_2$.

What is the ratio of the acceleration due to gravity on two planets with radii $R_1$ and $R_2$ and densities $\rho_1$ and $\rho_2$?

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