Two planets have radii R_1 and R_2 and densit | vedclass

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(A) 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

Vedclass · Accepted Answer

$R_1 \rho_1 : R_2 \rho_2$

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

Two planets have radii $R_1$ and $R_2$ and densities $\rho_1$ and $\rho_2$ respectively. Find the ratio of the acceleration due to gravity on these planets.

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