To locate centre of gravity by means of a plumbline

One of the best ways of finding the centre of gravity of a body is by use of a plumbline. Suppose, for example, we wish to find the centre of gravity of a flat irregularly shaped piece of cardboard. First of all, three small holes are made at well-spaced intervals round the edge of the card. A stout pin is then put through one of the holes and held firmly by a clamp and stand so that the card can swing freely on it (Fig. 6.8).

The card will come to rest ith its centre of gravity, G, vertically below the point of support. The vertical line through the support can now be located by means of a plumbline. A suitable plumbne is made from a length of cotton with a loop at one end and a weight tied at the ther. This is hung from the pin and the position of the cotton marked on the card two small pencil crosses. These crosses are joined by a pencil line.

The experiment is repeated with the card suspended by one of the other holes.
ince the centre of gravity lies on both of the lines drawn on the card, it must be
situated at their point of intersection. As a check, the card is suspended by the third hole. It should be found that, within .he limits of experimental error, the plumbline should pass through the intersection f the two lines.

The above method can be used to show that the centre of gravity of a triangular lamina lies at the point of intersection of its medians. (A median of a triangle is a line .Through one of the corners which bisects the opposite side.)