A circular plate of uniform thickness has a diameter of $$28$$ cm. A circular portion of diameter $$21$$ cm is removed from the plate as shown . O is the center of mass of complete plate. The position of center of mass of remaining portion will shift towards left from O by (in$$ $$cm)

Question

Infinity Learn · Accepted Answer

$$C1$$ is the center of mass of cut portion and $$C2$$ that of remaining portion. We have to find $$x2$$.$$x1=14$$−$$10.5=3.5cmMass$$ will be proportional to area. So mass of the whole disc is $$M=k$$$$π$$$$142Mass$$ of cut portion $$m1=k$$π(10.5)2Mass$$ of the remaining portion $$m2=M$$−$$m1=k$$$$π$$$$142$$−$$10.52=k$$π$$(24.5) ×(3.5) Now, $$m1x1=m2x2$$⇒ $$x2=m1x1m2=k$$π(10.5)2$$×$$3.5k$$π$$(24.5)×$$3.5=4.5cm$$

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A circular plate of uniform thickness has a diameter of 28 cm. A circular portion of diameter 21 cm is removed from the plate as shown . O is the center of mass of complete plate. The position of center of mass of remaining portion will shift towards left from O by (in cm)

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