Two thin circular discs of mass $m$ and $4 m$, having radii of $a$ and $2 a$, respectively are rigidly fixed by a massless, rigid rod of length $\mathrm{I}=\sqrt{24}$ a through their centers. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is $\omega$. The angular momentum of the entire assembly about the point ' O ' is $\overrightarrow{\mathrm{L}}$ (see the figure) Which of the following is statement(s) is (are) true?
