A uniform solid cylinder with radius R and length L has moment of inertia I 1 , about the axis of cylinder. A concentric solid cylinder of radius R ' = R 2 and length L ' = 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 I 1 I 2 = __________. (Both I 1 and I 2 are about the axis of the cylinder)

Step-by-step solution

Moment of inertia of solid cylinder of radius R and length L about the axis is I 1 = M 1 R 2 2 . Moment of inertia of carved out portion of the cylinder of radius R 2 and length L 2 is I 2 = M 2 R 2 2 2 = M 2 R 2 8 Now, the ratio I 1 I 2 = 4 M 1 M 2 As, mass = density × volume So, I 1 I 2 = 4 × ρ π R 2 L ρ π R 2 L 4 × 2 = 32