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Moment of inertia of identical rods joined into a cross or other shape

This type of question, asked 2 times: 2 Apr 2025, 21 Jan 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    2 Apr 2025

    16
    Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' α\alpha '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

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  2. Question 2

    21 Jan 2026 S1

    23
    Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is X12ML2\frac{X}{12}ML^{2}. The value of XX is ____\_\_\_\_ .