A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius $R(R << L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T, and its distance from the galaxy's axis is $r$, then :

Question

( A ) $T \propto \sqrt{r}$
( B ) $T^2 \propto r^3$
( C ) $T \propto r$
( D ) $T \propto r^2$