For a composite area consisting of a rectangle 100 mm x 60 mm with a semicircle of radius 30 mm removed from the top, the centroid of the composite area is located below the reference base by:
Choose the correct answer
Exactly 30 mm (always)
Computed as [A_rect x y_rect - A_semi x y_semi] / [A_rect - A_semi], where y values are measured from base
Equal to the centroid of the rectangle
At 50 mm from base
Correct Answer
B. Computed as [A_rect x y_rect - A_semi x y_semi] / [A_rect - A_semi], where y values are measured from base
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Composite centroid: y_bar = (A1 y1 - A2 y2)/(A1 - A2) for subtraction. A1 = 100x60 = 6000 mm2, y1 = 30 mm (from base); A_semi = pi x 30^2 / 2 = 1413.7 mm2, y_semi = 60 - 4r/(3pi) = 60 - 12.73 = 47.27 mm from base. y_bar = (6000x30 - 1413.7x47.27)/(6000-1413.7) = (180000 - 66817)/4586.3 = 24.68 mm from base.
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