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Concentric smaller cylinder carved out of a solid cylinder: ratio of moments of inertia about the axis

The same question, asked 2 times: 24 Jan 2023*, 24 Jan 2026 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    24 Jan 2023

    114
    A uniform solid cylinder with radius RR and length LL has moment of inertia I1I_{1}, about the axis of the cylinder. A concentric solid cylinder of radius R′=R2R^{'}=\frac{R}{2} and length L′=L2L^{'}=\frac{L}{2} is carved out of the original cylinder. If I2I_{2} is the moment of inertia of the carved-out portion of the cylinder then I1I2=\frac{I_{1}}{I_{2}}=(Both I1I_{1} and I2I_{2} are about the axis of the cylinder)

  2. Question 2

    24 Jan 2026 S2

    24
    A uniform solid cylinder of length LL and radius RR has moment of inertia about its axis equal to I1I_{1}. A small co-centric cylinder of length L/2L/2 and radius R/3R/3 carved from this cylinder has moment of inertia about its axis equals to I2I_{2}. The ratio I1/I2I_{1}/I_{2} is ____\_\_\_\_ .