Two thin circular discs of mass m and 4m, having radii of a and 2a,...

Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a massless, right rod of length $l = \sqrt{24}a$ through their center. 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 $\overset{\to}{L}$ (see the figure). Which of the following statement(s) is(are) true?
Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a massless,

Options

AThe magnitude of angular momentum of the assembly about its center of mass is $17m{a}^{2}\dfrac{\omega}{2}$
BThe magnitude of the z - component of $\overset{\to}{L}is55m{a}^{2}\omega$
CThe magnitude of angular momentum of center of mass of the assembly about the point O is 81 $m{a}^{2}\dfrac{\omega}{2}$
DThe center of mass of the assembly rotates about the z-axis with an angular speed of $\dfrac{\omega}{5}$

Correct answer

A. The magnitude of angular momentum of the assembly about its center of mass is $17m{a}^{2}\dfrac{\omega}{2}$

Step-by-step solution

Magnitude of angular momentum of the assembly about its centre of mass =

\dfrac{m{a}^{2}}{2}\omega + \dfrac{4m{\left(2a\right)}^{2}}{2}\omega = \dfrac{17m{a}^{2}}{2}\omega

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