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Question

# As shown in the figure, a circular sheet is removed from a uniform rectangular sheet. Find the horizontal distance of centre of mass of the remaining sheet from the origin O, after the removal of circular sheet. Use π=227 for calculation.

A
10.6 cm
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B
2.18 cm
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C
15.2 cm
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D
4.34 cm
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Solution

## The correct option is B 2.18 cmConsidering the circular sheet as the negative mass superimposed on the whole rectangular sheet, will give the new shape. Area of rectangular sheet A1=80 cm×40 cm=3200 cm2 Area of circular sheet A2=πr2=π×100 cm2=100π cm2 COM of the rectangular sheet is at origin O: (x1,y1)=(0,0) COM of the circular sheet (x2,y2)=(20,0) Replacing the respective shapes as point masses placed at their COM, x coordinate of COM of new shape is: xCM=A1x1−A2x2A1−A2 =(3200×0)−(100π×20)(3200)−(100π)=−2000π3200−100π ∴xCM=−440007202007=−2.18 cm Hence, COM of new shape is at a distance of 2.18 cm along−ve x-axis. Also, the COM of system will lie along the x-axis only, because system is symmetrical about x-axis as shown in figure.

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