The acceleration due to gravity near the surf | vedclass

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(C) 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 the planet can b

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$dR$

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(C) 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 the planet can be expressed in terms of its density $d$ and volume $V$ as $M = d 	imes V = d 	imes \frac{4}{3}\pi R^3$,we substitute this into the formula for $g$.$g = \frac{G(d 	imes \frac{4}{3}\pi R^3)}{R^2}$.Simplifying the expression,we get $g = \frac{4}{3}\pi G d R$.Since $\frac{4}{3}$,$\pi$,and $G$ are constants,it follows that $g \propto dR$.

The acceleration due to gravity near the surface of a planet of radius $R$ and density $d$ is proportional to

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