Question

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 the square of the time period will be proportional to

• A. $r^3$
• B. $r^2$
• C. $r^{2.5}$
• D. $r^{3.5}$

Answer 1

Answer: (D)

$\frac{m{v}^2}{r}=\frac{GMm}{r^{5/2}}$
$\left[\because F\propto \frac{1}{r^{5/2}}\right]$
or $r{\omega }^2=\frac{GM}{r^{5/2}}$
or $r\frac{4{\pi }^2}{T^2}=\frac{GM}{r^{5/2}}$
$T^2\propto r^{5/2}$ or $T^2\propto r^{3.5}$