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Moment of inertia of a disc after a part is cut out

This type of question, asked 3 times: 22 Jan 2025, 7 Apr 2025, 23 Jan 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    22 Jan 2025

    12
    A uniform circular disc of radius ' RR ' and mass ' MM ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2R/2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

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  2. Question 2

    7 Apr 2025

    100
    MM and RR be the mass and radius of a disc. A small disc of radius R/3 is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis AB passing through the center O and perpendicular to the plane of disc is 4xMR2\frac{4}{x}{MR}^{2}. The value of x is.

  3. Question 3

    23 Jan 2026 S2

    24
    Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by X256Mr2\frac{X}{256}{Mr}^{2}. The value of x is ____\_\_\_\_ .