Question

The radius of a planet is $R$. A satellite revolves around it in a circle of radius $r$ with angular speed $\omega$. The acceleration due to gravity on planet's surface will be :

• A. $\frac{r^{3} \omega}{R}$
• B. $\frac{r^{2} \omega^{3}}{R}$
• C. $\frac{r^{3} \omega^{2}}{R^{2}}$
• D. $\frac{r^{2} \omega^{2}}{R}$

Answer 1

Answer: (C)

Let $M$ be the mass of the planet and $m$ the mass of satellite
Then $m r \omega^{2}=\frac{G M m}{r^{2}}$
$\Rightarrow G M=r^{3} \omega^{2}$
$\Rightarrow g=\frac{G M}{R^{2}}=\frac{r^{3} \omega^{2}}{R^{2}}$