A uniform copper disk of radius \(R\) has a moment of inertia \(I\) around an axis passing through the center of the disk perpendicular to its plane. If the radius of the disk were only \(\dfrac{R}{2}\), but the thickness were the same, what would be the moment of inertia in terms of \(I\)? Hint: The moment of inertia of a solid disk about its center is \(\dfrac{1}{2} M R^{2}\).