Question

1. Locate the centroid of the shaded area. y = a cos TX L ㅏ늘 L 2 늘 →

Answer 1

solution:

4 a Equation of the curve, y = acos in Consider an elemental strip, which is at a distance of x units from the y-axis and whose dength is y units. So, the elemental area, dA-yak We know that the x-co-ordinate of the centroid is given by xdA Total area. A = 24 = var =2({ acos metu (1/1) - 21a [xdA = (xyada - 1 xacos acos =a[(xcosmety By using integration by parts, sin ſxdd = a + 47 2 -10 4712, at sin *(L) -cos: x-co-ordinate of the Centroid xdA ata x. im wiele We know that the y-co-ordinate of the centroid is given by radio Note: Here, instead of ydd, we have taken as dA because the centroidal distance of the elemental area from the y-axis is Nie [d4 = ch

1+cos 1 = dr - 2 2πχ sin L 27 L a 4 = x+ Jo szda - dA y-co-ordinate of the Centroid, y = a L Zaz 7 ra 8 πα 8 ye

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