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(D) The acceleration due to gravity $g$ at the surface of a planet of radius $R$ and density $\rho$ is given by the formula:$g = \frac{GM}{R^2}$Since

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

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(D) The acceleration due to gravity $g$ at the surface of a planet of radius $R$ and density $\rho$ 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 $\rho$ and volume $V = \frac{4}{3}\pi R^3$ as $M = \rho V = \rho \left(\frac{4}{3}\pi R^3\right)$,Substituting this into the expression for $g$:$g = \frac{G}{R^2} \left(\rho \cdot \frac{4}{3}\pi R^3\right) = \frac{4}{3}\pi G \rho R$Therefore,$g \propto \rho R$.For two planets,the ratio of their accelerations due to gravity is:$\frac{g_1}{g_2} = \frac{\rho_1 R_1}{\rho_2 R_2}$Thus,$g_1:g_2 = R_1\rho_1:R_2\rho_2$.

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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