A semicircular portion of radius r=10cm is cut from a uniform rectangular plate as shown in the figure. The distance of center of mass C of the remaining plate, from point O is (COM of semicircle is at distance 4r3π from the base)
A
7.75cm
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B
5cm
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C
17cm
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D
4.6cm
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Solution
The correct option is A7.75cm Remaining area = Area of rectangle - Area of semicircular portion,
Area of rectangle A1=2r2 Area of semicircular portion A2=πr22
If r1 and r2 are the positions of centre of mass of the rectangle and the semicircular portion with respect to O. r1=−r2 and r2=−4r3π (left of origin is taken -ve)
Therefore, center of mass of remaining portion =A1×(−r2)−A2×(−4r3π)A1−A2