Question

drive the center of mass of semi circular plate
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Answer 1

Explanation:

The center of mass of a uniform half-disk obviously lies on the perpendicular bisector of the base diameter, at distance dd from the centre of the disk. By the Pappus centroid theorem,

2πd⋅π2R2=4π3R3,2πd⋅π2R2=4π3R3,

hence d=4R3πd=4R3π.