Question

The radius of a planet is $R$. A satellite revolves around it in a circle of radius $r$ with angular velocity ${\omega }_0$. The acceleration due to the gravity on planet's surface is

• A. $\frac{r^3{\omega }_0}{R}$
• B. $\frac{r^3{\omega }_0^3}{R^2}$
• C. $\frac{r^3{\omega }_0^3}{R}$
• D. $\frac{r^3{\omega }_0^2}{R^2}$

Answer 1

Answer: (D)

$\frac{r^3{\omega }_0^2}{R^2}$

$\frac{GMm}{r^2}=m{\omega }_0^{2}r$
$\Rightarrow GM={\omega }_0^2{r}^3$
$\Rightarrow g{R}^2={\omega }_0^2{r}^3$
$\Rightarrow g=\frac{{\omega }_0^2{r}^3}{R^2}$