Two planets of radii in the ratio 2 : 3 are m | vedclass

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(A) The acceleration due to gravity $g$ at 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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$1$

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(A) The acceleration due to gravity $g$ at 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 $ho$ and radius $R$ as $M = ho 	imes V = ho 	imes \frac{4}{3}\pi R^3$,we can substitute this into the formula for $g$:$g = \frac{G(ho \cdot \frac{4}{3}\pi R^3)}{R^2} = \frac{4}{3}G\pi ho R$.Therefore,the ratio of acceleration due to gravity for two planets is $\frac{g_1}{g_2} = \frac{ho_1}{ho_2} 	imes \frac{R_1}{R_2}$.Given the ratios $\frac{R_1}{R_2} = \frac{2}{3}$ and $\frac{ho_1}{ho_2} = \frac{3}{2}$,we substitute these values:$\frac{g_1}{g_2} = \frac{3}{2} 	imes \frac{2}{3} = 1$.Thus,the ratio of acceleration due to gravity at the surface of the two planets is $1$.

Two planets of radii in the ratio $2 : 3$ are made from the material of density in the ratio $3 : 2$. Then the ratio of acceleration due to gravity $g_1/g_2$ at the surface of the two planets will be

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