A flat surface of a thin uniform disk A of radius R is glued to a...

The centre of mass of $B$ has angular velocity $\omega$ about the centre of $A$. Therefore, the velocity of the centre of $B$ is

${V}_{B} = \omega2R$.

The point of contact of $A$ and $B$ is at rest therefore, the angular velocity of $B$ will be,

${\omega}_{B} = \dfrac{{v}_{B}}{R} = 2\omega$

Now the angular momentum of $B$ with respect to centre of $A$

$L = M{v}_{B}r + {I}_{CM}{\omega}_{B}$

$⇒ L = M\omega2R2R + \dfrac{M{R}^{2}}{2}2\omega$

$L = 5M{R}^{2}\omega$

Comparing the magnitude with $nM\omega{R}^{2}$

$n = 5$