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?
Select ALL correct options:
A
The center of mass of the assembly rotates about the $z$-axis with an angular speed of $\omega / 5$.
B
The magnitude of angular momentum of center of mass of the assembly about the point O is $81 \mathrm{ma}^2 \omega$
C
The magnitude of angular momentum of the assembly about its center of mass is $17 \mathrm{ma}^2 \omega / 2$
D
The magnitude of the $z$-component of $\left[\right.$ is $55 \mathrm{ma}^2 \omega$
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