A flat surface of a thin uniform disk $A$of radius$R$ is glued to a horizontal table. Another thin uniform disk$B$ of mass $M$and with the same radius $R$rolls without slipping on the circumference of $A$, as shown in the figure. A flat surface of $B$ also lies on the plane of the table. The center of mass of$B$ has fixed angular speed $\omega$about the vertical axis passing through the center of $A$. The angular momentum of $B$ is $nM\omega R^2$with respect to the center of $A$. Which of the following is the value of $n$?

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.