Centroid and centroid of gravity

Centroid  :

The plane figures (like triangle, quadrilateral, circle etc.) have only areas, but no mass. The centre of area of such figures is known as centroid. The method of finding out the centroid of a figure is the same as that of finding out the centre of gravity of a body.

 (or)

The centroid of a solid body made from a single material is the center of its mass. If the mass of a body is distributed evenly, then the centroid and center of mass are the same. The centroid of a body is the point where there is equal volume on all sides.

 (or)

     It is the point at which total area of the plane (or) Lamina is acting.

Where

$$\bar{x} = \frac{A_{1}X_{1}+A_{2}X_{2}+ …..}{A_{1}+A_{2}}$$

$$\bar{y} = \frac{A_{1}Y_{1}+A_{2}Y_{2}+ …..}{A_{1}+A_{2}}$$

Where ‘A’ is area of the plane

Centroid of Gravity :

It is the point at which the total volume (or) total weight (or) total mass is acting.

Centre of gravity applies to solids.

Solids like cone, cylinder and sphere

Centroid is for planes /lamina's /area.

The centre of gravity (or centroid) may be found out by any one of the following methods:
1. By geometrical considerations
2. By moments
3. By graphical method