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Asked by arup.isro | 19 Dec, 2018, 10:54: PM
Let us first get the Centre of mass of semicircular plate.
As shown in figure,  let us divide the semi circular plates into strips of width dr parallel to diameter.
Let us consider a strip of length 2l at a distance r from center as shown in figure.
Mass of this strip = ρ×2l×dr , where ρ is density which is expressed as mass per unit area.

Center of mass of semi-circular plate :
Let A be the centre of mass of rectangular plate,  B is the centre of mass of semicircular plate and
P is the center of mass of plate after cutting the semi-circle.

we have OA = r/2  and OB = [ 4/(3π) ] r

Center of mass of plate after cutting semi-circle is calculated as follows

mA × OA = mB × OB + mP × OP

where mA is mass of full rectangular plate = ρ×2r2
mB is mass of semi-circular plate = ρ×(π/2)×r2
mP is mass of plate after cutting semi-circle = ρ× [ 2 - (π/2) ]×r2

Hence
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