Question

An artificial satellite revolves around a planet for which gravitational force $(F)$ varies with distance $r$ from its centre as $F \propto r^2$. If $v_0$ its orbital speed, then

• A. $v_{0} \propto r^{-1 / 2}$
• B. $v_{0} \propto r^{3 / 2}$
• C. $v_{0} \propto r^{-3 / 2}$
• D. $v_{0} \propto r$.

Answer 1

Answer: (B)

Gravitational force $(F)$ provides the necessary centripetal force to keep the satellite in orbit,
$\Rightarrow \frac{m v_{0}^{2}}{r} \propto F $
$\frac{m v_{0}^{2}}{r} \propto r^{2} $
$v_{0} \rightarrow$ Orbital speed
$ r \rightarrow $ Radius of orbit
$\Rightarrow v_{0} \propto r^{3 / 2}$