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Coordinate of centes of mass (c.o.m) is given by X_cm = integral x dm/integral dm Y_cm = integral y dm/integral dm For X_cm mass of elementary area dA = dx times 30 dm = 16 kg/(200 times 30) cm^2 times [30 times dx] dm = 16 times 30/200 times 30 dx implies dm = 2/25 dx centre of mass of elementary area (x, 15) X_cm = integral x dm/integral dm X_cm = integral x middot 2/25 dx/16 X-cm = 2/16 times 25 integral^200_0 x dx X_cm = 1/200 [x^2/2]^200_0 X_cm = 1/200 [200 times 200/2] X-cm = 100 (B) Similarly Y_cm = 15 cm I = integral r^2 dm dm = 18 times 30 times dx/(100 times 30) dm = 2/25 times dx I = integral^100_-100 x^2 middot 2/25 dx I = 2/25 [x^3/3]^100_-100 = 2000000/3 I = 160000/3 kg - cm^2 (c) case II axis theore I = I_cm + md^2
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