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Ratio of moments of inertia of bodies of equal mass but different density or size

This type of question, asked 3 times: 4 May 2023 S2, 9 May 2024 S1, 20 Apr 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    7
    Two solid spheres (A and B) are made of metals having densities ρA\rho_A and ρB\rho_B respectively. If their masses are equal then ratio of their moments of inertia IBIA\frac{I_B}{I_A} about their respective diameter is

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  2. Question 2

    9 May 2024 S1

    34
    Two discs of same mass and same thickness (tt) are made from two different materials of densities 'd1d_1' and 'd2d_2' respectively. The ratio of the moment of inertia I1I_1 to I2I_2 of two discs about an axis passing through the centre and perpendicular to the plane of disc is

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  3. Question 3

    20 Apr 2025 S1

    5
    Two discs A and B of same material and thickness have radii R and 3 R respectively. Their moments of inertia about their axis will be in the ratio

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