Answer
The rotational inertia of each object is $~~I = \frac{1}{2}MR^2$
Work Step by Step
We can write an expression for the rotational inertia of the solid cylinder:
$I = \frac{1}{2}MR^2$
We can write an expression for the rotational inertia of the thin hoop:
$I = M(\frac{R}{\sqrt{2}})^2 = \frac{1}{2}MR^2$
The rotational inertia of each object is $~~I = \frac{1}{2}MR^2$
