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Two spheres joined by a rod: moment of inertia about the centre of one sphere

The same question, asked 2 times: 10 May 2024 S2*, 20 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S2

    29
    Two spheres each of mass 'MM' and radius R2\frac{R}{2} are connected at the ends of massless rod of length '2R2R'. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

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  2. Question 2

    20 Apr 2025 S1

    40
    Two spheres each of mass MM and radius RR are connected with a massless rod of length 4 R . The moment of inertia of the system about an axis passing through the center of one of the spheres and perpendicular to the rod will be

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