Consider a circular disc of radius 20 cm with centre located at the… | JEE Main 2025 (23 Jan, Shift 1)

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Composite & Cut-Out Bodies

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of 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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Answer: (d)

Hole touches the edge, so its centre is at $20 - 5 = 15$ cm from O. Mass $\propto$ area $\propto r^2$ .
Disc: $20^2 = 400$ units at $x=0$ ; hole: $5^2 = 25$ units at $x = 15$ cm.
$x_{cm} = \frac{400(0) - 25(15)}{400-25} = -\frac{375}{375} = -1$ cm
So the answer is (d) $1.0$ cm (on the side opposite the hole).

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