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7.Gravitation
normal
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
$\frac{r^3\omega _0^3}{ R}$
C
$\frac{r^3\omega _0^2}{ R}$
D
$\frac{r^3\omega _0^2}{ R^2}$
Solution
As, $F=m a$ $\frac{G M m}{r^{2}}=m \omega_{0}^{2} r$
$G M=\omega_{0}^{2} r^{3}$
$F=m a$
$a=\frac{F}{m}$
$a=\frac{G M}{R^{2}}=\frac{\omega_{0}^{2} r^{3}}{R^{2}}$
Standard 11
Physics