Q.

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

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a

-r2(π-14)

b

-r4(π-14)

c

-r4(π-12)

d

-3r4(π-14)

answer is C.

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Detailed Solution

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 = (πr2)σ(0)+l2(-σ)(r2)πr2σ+l2(-σ)        = -l2r2(πr2-l2)= -r222(πr2-r22) = -r4(π-12)
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