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(D) The acceleration due to gravity $g$ at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since the mass $M$ of a planet can be expressed in

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 $g$ at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since the mass $M$ of a planet can be expressed in terms of its density $ho$ and radius $R$ as $M = ho 	imes V = ho 	imes \frac{4}{3} \pi R^3$,we substitute this into the formula for $g$:$g = \frac{G (ho \cdot \frac{4}{3} \pi R^3)}{R^2} = \frac{4}{3} \pi G ho R$.This shows that $g \propto ho R$.Therefore,the ratio of the accelerations due to gravity for the two planets is $\frac{g_1}{g_2} = \frac{ho_1 R_1}{ho_2 R_2}$.Thus,$g_1 : g_2 = R_1 ho_1 : R_2 ho_2$.

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively $\rho_1$ and $\rho_2$. The ratio of the accelerations due to gravity at their surfaces is

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