The centroid of an area is the mean position of elements of area. The coordinates of centriod is mean value of coordinates of all the elemental points in the area. The centre of mass is the mean position of elements of mass. In a uniform gravitational field, the gravitational force acts through the centre of mass. But, if the gravitational field (hypothetically) is not uniform (in the case of very large body), centre of mass and centre of gravity will be different. Similarly, if the mass per unit area of a shape varies, the centre of mass would not coincide with the centroid. Centroid is a mathematical, geometric concept, i.e., the geometric centre of a body. It can be calculated as the centre of mass of an object with constant density throughout the body.
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