Centre of Gravity

 CENTRE OF GRAVITY

The point at which the whole mass or weight of Body is supposed to act, irrespective of the position of the Body is known as centre of gravity. It is generally written as C.G. and denoted by letter ‘G’. The term centre of gravity is applied to the solid body having Volume. {e.g. Cone, Cylinder, Sphere, Hemisphere etc.)

Cone	Cylinder	Sphere	Hemisphere

 CENTROID

The point at which the entire area of a plane lamina or plane figure is supposed to be acting, irrespective of the position of lamina is known as centroid or centre of area of body. It is generally denoted by letter ‘C’ or ‘G’. The term centroid is applied to the plane figures having Area. {e.g. plane figures like triangle, rectangle, square, circle. Semicircle, trapezium, quadrilateral, etc.)

Circle	Triangle	Rectangle	Trapezium

 

 CENTRE OF GRAVITY OF PLANE FIGURES

The plane geometrical figures (such as T-section, I-section, L-section etc.) have only areas but no mass. The centre of gravity of such figures is found out in the same way as that of solid bodies. The centre of area of such figures is known as centroid, and coincides with the centre of gravity of the figure.

Let X and Y be the co-ordinates of the centre of gravity with respect to some axis of reference, then

        

Where a₁, a₂, a₃……. etc; are the areas into which the whole figure is divided

x₁, x₂, x₃……. etc; are the respective co-ordinates of the areas a₁, a₂, a₃……. on X-X axis with respect to same axis of reference.

y₁, y₂, y₃……. etc; are the respective co-ordinates of the areas a₁, a₂, a₃……. on Y-Y axis with respect to same axis of reference.