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Seven touching discs or rings in a hexagonal pattern: moment of inertia about the centre

This type of question, asked 2 times: 10 May 2024 S1, 18 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    10 May 2024 S1

    22
    Seven identical discs, each of mass MM and radius RR, are arranged in a hexagonal plane pattern so as to touch each neighbouring disc, as shown in the figure. The moment of inertia of the system of seven discs about an axis passing through the centre of the central disc and normal to the plane of all discs is

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  2. Question 2

    18 Apr 2026 S2

    105
    Given identical rings are arranged in a hexagonal plane pattern so as to touch each neighbouring ring as shown in figure. Each ring has mass M and radius R. The moment of inertia of the system of seven rings about an axis passing through the centre of central ring and normal to plane of all rings is

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