If two planets have their radii in the ratio | vedclass

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

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$mx : ny$

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(D) The acceleration due to gravity $g$ on 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 $d$ and radius $R$ as $M = \frac{4}{3} \pi R^3 d$,we substitute this into the formula for $g$:$g = \frac{G}{R^2} \left( \frac{4}{3} \pi R^3 d ight) = \frac{4}{3} \pi G R d$.This shows that $g \propto R \cdot d$.Given the ratios of radii $\frac{R_1}{R_2} = \frac{x}{y}$ and densities $\frac{d_1}{d_2} = \frac{m}{n}$,the ratio of the acceleration due to gravity is:$\frac{g_1}{g_2} = \frac{R_1}{R_2} 	imes \frac{d_1}{d_2} = \frac{x}{y} 	imes \frac{m}{n} = \frac{xm}{yn}$.Thus,the ratio is $xm : yn$ or $mx : ny$.

If two planets have their radii in the ratio $x: y$ and densities in the ratio $m: n$,then the ratio of the acceleration due to gravity on them is

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