Two thin circular discs of mass $m$ and $4m$,having radii of $a$ and $2a$,respectively,are rigidly fixed by a massless,rigid rod of length $l=\sqrt{24}a$ 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 $\vec{L}$ (see the figure). Which of the following statement$(s)$ is(are) true?
$(A)$ 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 $81ma^2\omega$
$(C)$ The magnitude of angular momentum of the assembly about its center of mass is $17ma^2\omega/2$
$(D)$ The magnitude of the $z$-component of $\vec{L}$ is $55ma^2\omega$

• A
  $A, C$
• B
  $A, B$
• C
  $A, D$
• D
  $D, C$