A physical pendulum consists of a uniform rigid rod of length \(L\) and mass \(M\) pivoted frictionlessly at one end, with a small object of mass \(m\) affixed to its free end.

For small-amplitude oscillations, the period of the system is given by
\[ T = 2\pi \sqrt{\dfrac{2M + 6m}{3M + 6m}\dfrac{L}{g}} \]

Which of the following statements correctly describes the limiting behavior of the period \(T\) and provides the correct physical justification?