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(B) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{GM}{r^2}$.Since the mass $M$ of a planet can be

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$r_1 \varrho_1: r_2 \varrho_2$

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(B) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{GM}{r^2}$.Since the mass $M$ of a planet can be expressed in terms of its density $\varrho$ and radius $r$ as $M = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi r^3 \varrho$,we substitute this into the formula for $g$:$g = \frac{G (\frac{4}{3} \pi r^3 \varrho)}{r^2} = \frac{4}{3} \pi G r \varrho$.Therefore,$g \propto r \varrho$.For planet $A$,$g_A \propto r_1 \varrho_1$.For planet $B$,$g_B \propto r_2 \varrho_2$.The ratio of acceleration due to gravity on $A$ to that of $B$ is $\frac{g_A}{g_B} = \frac{r_1 \varrho_1}{r_2 \varrho_2}$.

Two planets $A$ and $B$ have densities $\varrho_1$ and $\varrho_2$ and have radii $r_1$ and $r_2$ respectively. The ratio of acceleration due to gravity on $A$ to that of $B$ is:

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