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The radius of a planet is R. A satellite revolves around it in a circle of radius r with angular velocity $ω_{0} .$ The acceleration due to the gravity on planet’s surface is

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$\frac{r^{3} ω_{0}^{2}}{R^{2}}$

$\frac{r^{3} ω_{0}^{3}}{R^{2}}$

$\frac{r^{3} ω_{0}}{R}$

$\frac{r^{3} ω_{0}^{2}}{R}$

answer is D.

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Detailed Solution

$\frac{G M m}{r^{2}} = m r w_{0}^{2}$
$G M = r^{3} w_{0}^{2}$
Acceleration due to gravity on the surface of the planet is $g = \frac{G M}{R^{2}} = \frac{r^{3} w_{0}^{2}}{R^{2}}$

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