The diameters of two planets are in the ratio | vedclass

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(C) The gravitational acceleration $g$ on the surface of a planet is given by $g = \frac{GM}{R^2}$.Since $M = \rho \cdot V = \rho \cdot \frac{4}{3}\pi

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$2 : 1$

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(C) The gravitational acceleration $g$ on the surface of a planet is given by $g = \frac{GM}{R^2}$.Since $M = \rho \cdot V = \rho \cdot \frac{4}{3}\pi R^3$,substituting this into the formula gives $g = \frac{G \cdot \rho \cdot \frac{4}{3}\pi R^3}{R^2} = \frac{4}{3} \pi G \rho R$.Thus,$g \propto \rho R$.Given the ratio of diameters $D_1 : D_2 = 4 : 1$,the ratio of radii $R_1 : R_2 = 4 : 1$.Given the ratio of densities $\rho_1 : \rho_2 = 1 : 2$.The ratio of gravitational accelerations is $\frac{g_1}{g_2} = \frac{\rho_1 R_1}{\rho_2 R_2} = \left(\frac{1}{2}\right) \cdot \left(\frac{4}{1}\right) = \frac{4}{2} = 2 : 1$.

The diameters of two planets are in the ratio $4:1$. Their mean densities have the ratio $1:2$. The ratio of gravitational acceleration on the surface of the planets will be:

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