The radii of two planets A and B are R and 4R | vedclass

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(C) The acceleration due to gravity $g$ at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since mass $M = 	ext{density} (ho) 	imes 	ext

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$3:4$

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(C) The acceleration due to gravity $g$ at the surface of a planet is given by $g = \frac{GM}{R^2}$.Since mass $M = 	ext{density} (ho) 	imes 	ext{volume} (V) = ho 	imes \frac{4}{3} \pi R^3$,we can write:$g = \frac{G}{R^2} 	imes ho 	imes \frac{4}{3} \pi R^3 = \left( \frac{4}{3} \pi G ight) ho R$.Therefore,$g \propto ho R$.For planet $A$: $g_A \propto ho 	imes R$.For planet $B$: $g_B \propto \frac{ho}{3} 	imes 4R = \frac{4}{3} ho R$.Taking the ratio:$\frac{g_A}{g_B} = \frac{ho R}{\frac{4}{3} ho R} = \frac{1}{4/3} = \frac{3}{4}$.Thus,the ratio $(g_A : g_B)$ is $3:4$.

The radii of two planets $A$ and $B$ are $R$ and $4R$ and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be

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