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Moment of inertia of point masses at the corners of a square or triangle

This type of question, asked 4 times: 16 May 2023 S2, 19 Apr 2025 S1, 25 Apr 2025 S1, 17 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    16 May 2023 S2

    3
    Three point masses, each of mass mm, are placed at the corners of an equilateral triangle of side LL. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices will be

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  2. Question 2

    19 Apr 2025 S1

    20
    Four particles each of mass M are placed at the corners of a square of side L . The radius of gyration of the system about an axis perpendicular to the square and passing through its center is

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  3. Question 3

    25 Apr 2025 S1

    12
    Four particles each of mass M are placed at the corners of a square of side L . The radius of gyration of the system about an axis perpendicular to the square and passing through its center is

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  4. Question 4

    17 Apr 2026 S1

    105
    Four point masses m, 2m, 3m and 4m are kept at the corners A, B, C and D respectively of a square ABCD of side 'bb'. The moment of inertia of the system about an axis perpendicular to the plane of the square and passing through the point D is

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