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Centre of mass of a disc with a circular hole cut out

This type of question, asked 2 times: 2021 Paper 2, 23 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 2

    5
    A circular hole of radius (a2)\left( \frac{a}{2} \right) is cut out of a circular disc of radius ' aa ' shown in figure. The centroid of the remaining circular portion with respect to point ' OO ' will be:

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  2. Question 2

    23 Jan 2025

    20
    Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of a radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be-

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