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Moment of inertia of a frame made of thin rods

This type of question, asked 5 times: May 2021 S1, 9 May 2023 S2, 11 May 2023 S2, 15 May 2023 S1, 15 May 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    49
    Three identical thin rods each of length ll and mass MM are joined together to form a letter H. What is the moment of inertia of the system about one of the sides of H?

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  2. Question 2

    9 May 2023 S2

    47
    Three thin rods, each mass '2M' and length 'L' are placed along x, y and z axis which are mutually perpendicular. One end of each rod is at origin. Moment of inertia of the system about x-axis is

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  3. Question 3

    11 May 2023 S2

    12
    Four thin metal rods each of mass 'M' and length 'L', are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

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  4. Question 4

    15 May 2023 S1

    16
    Three thin rods, each of mass MM and length LL are placed along X, Y and Z axes which are mutually perpendicular. One end of each rod is at origin. M.I. of the system about Z axis is

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  5. Question 5

    15 May 2026 S1

    105
    A square frame ABCD is formed by 4 identical rods each of mass mm and length ℓ\ell. This frame is in XY plane such that side AB coincides with x-axis and side AD along y-axis. The moment of inertia of the frame about x-axis is

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