You must have tried to balance your exercise book, saucer or a piece of card board on your finger tips. It will be found that in each case, there is one and only one point at which these objects can be balanced.
The point through which the resultant of the weights of all the particles of the body acts is called its centre of gravity.
In problems where the weight of a body has to be taken into account, that weight is considered as a single force acting vertically downwards through the centre of gravity of the body.
Experiment :
Aim :
To determine the centre of gravity of an irregularly shaped lamina using a plumb line.
Procedure :
Make three holes near the edge of the lamina so that the lamina swings freely when pivoted from each hole. Hang the lamina about one of its holes on a pin clamped on a retort stand.
C.G. of an irregular body
Suspend a plumb line from P and mark the position PP' on the lamina.
Repeat the experiment by suspending the lamina from Q and R and similarly mark the plumb line positions QQ' and RR'. You will observe that all the three lines, PP', QQ' and RR' intersect at one point. This point of intersection of these lines is the centre of gravity of the lamina.
Centre of gravity of geometrically shaped objects will lie in the geometric centre. The centre of gravity of different geometrically shaped objects are shown in figure below.
C.G. of solids of different regular shapes
The centre of gravity of some objects are given below in table below:
| Object | C.G | |
|---|---|---|
| a. | Uniform straight wire | the mid point |
| b. | Uniform beam or rod | the mid point of the axis |
| c. | Circle | the center of the circle |
| d. | Ring | its center |
| e. | Triangle | Centroid |
| f. | rectangle | intersecton of its diagonals |
| g. | rhombus | intersecton of its diagonals |
| h. | Sphere | its center |
| i. | Solid cone | 1/4th of its height from its base |
| j. | hollow cone | 1/3rd of its height from its base |
| k. | cube/cuboid | the mid point of the line joining the centers of opposite sides |
