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Moment of inertia of masses or spheres placed at the corners of a square

This type of question, asked 3 times: 2021 Paper 5, 2021 Paper 25, 27 Jan 2024. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 5

    11
    Four equal masses, mm each are placed at the corners of a square of length (l)(l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be:

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  2. Question 2

    2021 Paper 25

    5
    Four identical solid spheres each of mass ' mm ' and radius ' aa ' are placed with their centres on the four corners of a square of side ' bb '. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is:

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  3. Question 3

    27 Jan 2024

    26
    Four particles each of mass 1 kg1\text{ }kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is ___ kgm2kgm^{2}.