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

$\begin{array}{1 1} T^2 \alpha r^3 \\ T \alpha r^2 \\ T \alpha r \\ T \alpha \sqrt {r} \end{array} $