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Moments of inertia of discs of the same material with different radius or thickness

This type of question, asked 3 times: 31 Jan 2023, 28 Jan 2025, 22 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    31 Jan 2023

    119
    Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm1\text{ }cm and 0.5 cm0.5\text{ }cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of x6\frac{x}{6}. The value of xx is____

  2. Question 2

    28 Jan 2025

    24
    Two iron solid discs of negligible thickness have radii R1R_{1} and R2R_{2} and moment of inertia I1I_{1} and I2I_{2}, respectively. For R2=2R1R_{2}= 2R_{1}, the ratio of I1I_{1} and I2I_{2} would be 1/x1/x, where x=x = ____\_\_\_\_

  3. Question 3

    22 Jan 2026 S1

    24
    A circular disc has radius R1R_{1} and thickness T1T_{1}. Another circular disc made of the same material has radius R2R_{2} and thickness T2T_{2}. If the moment of inertia of both discs are same and R1R2=2\frac{R_{1}}{R_{2}} = 2 then T1T2=1α\frac{T_{1}}{T_{2}} = \frac{1}{\alpha}. The value of α\alpha is ____\_\_\_\_ .