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we can use direct formula for center of mass of remaining portion ...
rcom = [(A1r1 - A2r2) / A1-A2 ]
this formula is with respect to some point , so take center of circle as origin...
A1,A2 are area;s of complete body , removed part ...
r1,r2 are the center of mass of these two parts ...
A1 = area of square = A2 (from figure , radius = side of square)
removed area = piA2/4 (area of quater circle)
r1 = A/sqrt2 (center of mass of square lies at center of square)
r2 = 4root2R/3pi (this is the derived result , center of mass of quater disk lies at 4root2 R/3pi )
r2 = 4root2 A/3pi (since R = A)
now plugging all these values in the formula
rcom = A [ 1/root2 - root2/3]/(1-pi2/4)
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