A disc (of$$ radius r $$cm) of uniform thickness and uniform density σ has a square hole with sides of length I $$=$$ $$r2$$ cm. One corner of the hole is located at the centre of the disc and centre of the hole lies on $$y-axis$$ as shown. Then the $$y-coordinate$$ of position of centre of mass of disc with hole (in$$ $$cm) is

Question

A disc (of$$ radius r $$cm) of uniform thickness and uniform density σ has a square hole with sides of length I $$=$$ $$r2$$ cm. One corner of the hole is located at the centre of the disc and centre of the hole lies on $$y-axis$$ as shown. Then the $$y-coordinate$$ of position of centre of mass of disc with hole (in$$ $$cm) is

Infinity Learn · Accepted Answer

This disc can be assumed to be made of a complete uniform disc and a square plate with same negative mass density.Ycm $$=$$ $$m1y1+m2y2m1+m2$$ $$=$$ $$($$π$$r2)$$σ(0)+l2(-$$σ$$)(r2)π$$r2$$σ$$+l2(-$$σ$$)$$        $$=$$ $$-l2r2($$π$$r2-l2)=$$ $$-r222($$π$$r2-r22)$$ $$=$$ $$-r4($$π$$-12)$$

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