Answer
$\frac{5}{8}MR^2$
Work Step by Step
We add the inertias of the inner and outer rings using the equation for the moment of inertia of a ring:
$ I =(\frac{1}{2}M)(\frac{1}{2}R)^2+(\frac{M}{2})R^2=\frac{5}{8}MR^2$
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