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# 10 years ago

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)