Two planets have the same average density but | vedclass

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(A) 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

$\frac{g_1}{g_2} = \frac{R_1}{R_2}$

Vedclass · Answer

(A) 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 density $\rho$ and radius $R$ as $M = \rho \cdot V = \rho \cdot \frac{4}{3}\pi R^3$,we substitute this into the gravity formula:$g = \frac{G}{R^2} \cdot (\rho \cdot \frac{4}{3}\pi R^3) = \frac{4}{3}\pi \rho GR$.Given that the average density $\rho$ is the same for both planets,we have $g \propto R$.Therefore,the ratio of the acceleration due to gravity on the two planets is $\frac{g_1}{g_2} = \frac{R_1}{R_2}$.

Two planets have the same average density but their radii are $R_1$ and $R_2$. If acceleration due to gravity on these planets be $g_1$ and $g_2$ respectively,then

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