# Centre of Gravity and Equilibrium

#### Centre of Gravity

The centre of gravity of an object is a point where the resultant gravitational force acting on the body may be taken to act. For objects of uniform thickness lying in a horizontal plane, the centre of gravity is vertically in line with the point of balance of the object. For a thin uniform rod the point of balance and hence the centre of gravity is halfway along the rod as shown in Figure 10.1(a).

A thin flat sheet of a material of uniform thickness is called a lamina and the centre of gravity of a rectangular lamina lies at the point of intersection of its diagonals, as shown in Figure 10.1(b). The centre of gravity of a circular lamina is at the centre of the circle, as shown in Figure 10.1(c).

Equilibrium

An object is in equilibrium when the forces acting on the object are such that there is no tendency for the object to move. The state of equilibrium of an object can be divided into three groups.

(i) If an object is in stable equilibrium and it is slightly disturbed by pushing or pulling (i.e. a disturbing force is applied), the centre of gravity is raised and when the disturbing force is removed, the object returns to its original position. Thus a ball bearing in a hemispherical cup is in stable equilibrium, as shown in Figure 10.2(a).

(ii) An object is in unstable equilibrium if, when a disturbing force is applied, the centre of gravity is lowered and the object moves away from its original position. Thus, a ball bearing balanced on top of a hemispherical cup is in unstable equilibrium, as shown in Figure 10.2(b).

(iii) When an object in neutral equilibrium has a disturbing force applied, the centre of gravity remains at the same height and the object does not move when the disturbing force is removed. Thus, a ball bearing on a flat horizontal surface is in neutral equilibrium, as shown in Figure 10.2(c).