Q: Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. if the gravitational force of attraction between the planet and the star is proportional to R-5/2, then
(a)T2 is proportional to R2
(b)T2 is proportional to R7/2
(c)T2 is proportional to R3/2
(d)T2 is proportional to R3.75
Ans: (b)
Sol: $\large \frac{mv^2}{R} \propto R^{-5/2}$
$\large v \propto R^{-3/4}$
$\large T = \frac{2\pi R}{v}$
$\large T^2 \propto (\frac{R}{v})^2$
$\large T^2 \propto (\frac{R}{R^{-3/4}})^2$
$\large T^2 \propto R^{7/2}$