The diameters of two planets are in the ratio | vedclass

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(C) 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

Vedclass · Accepted Answer

$2:1$

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(C) 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 mean 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 $g$:$g = \frac{G}{R^2} 	imes (ho 	imes \frac{4}{3}\pi R^3) = \frac{4}{3}G\pi Rho$.Therefore,the ratio of acceleration due to gravity for two planets is:$\frac{g_1}{g_2} = \frac{R_1 ho_1}{R_2 ho_2} = \left(\frac{R_1}{R_2}ight) 	imes \left(\frac{ho_1}{ho_2}ight)$.Given that the ratio of diameters is $4:1$,the ratio of radii $\frac{R_1}{R_2}$ is also $4:1$.Given that the ratio of mean densities $\frac{ho_1}{ho_2}$ is $1:2$.Substituting these values:$\frac{g_1}{g_2} = \left(\frac{4}{1}ight) 	imes \left(\frac{1}{2}ight) = \frac{4}{2} = \frac{2}{1}$.Thus,the ratio is $2:1$.

The diameters of two planets are in the ratio $4 : 1$ and their mean densities in the ratio $1 : 2$. The acceleration due to gravity on the planets will be in the ratio:

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