A uniform solid cylinder with radius \( R \) and length \( L \) has moment of inertia \( I_1 \), about the axis of the cylinder. A concentric solid cylinder of radius \( R' = \frac{R}{2} \) and length \( L' = \frac{L}{2} \) is carved out of the original cylinder. If \( I_2 \) is the moment of inertia of the carved out portion of the cylinder then \( \frac{I_1}{I_2} = \) ________ . (Both \( I_1 \) and \( I_2 \) are about the axis of the cylinder)
