Question

(e) For the centroid shown below: (i) Explain why, in this case, it is only necessary to find the position of the centroid along one axis. (ii) Find the centroid of the area shown, relative to point O, at the left hand end. 120 mm dia, hole 400 mm 100 mm 100 mm 100 mm

Answer 1

e) i) As the given figure is already symmetrical about line x= 100 mm, we don't need to find the position of the centroid of lamina along x-axis as it is quite obvious that the centroid lies on x= 100 mm, the following work proves this argument.

a) Xcm = A,,, + A₂X2 A, + A2 XCM = (200x400) 100 + (-7 x 120°) 100 (200x400) + (-m x 120) considering the area of hole as the negative area. Hence, nom = 100 mm Similarly, You A,Y, + A2Y2 Ait Az. Yem: (200x400) 200 - (Tax 120°) x 100 (200x400) – (V x 120%) Yem = 216.46 mm Hence, the centersid is (100mm, 216.46 mm)