Determine the centre of gravity of plane lamina by pivoting method.

Explanation

We can determine the centre of gravity of a uniform lamina of even an irregular shape by pivoting it at various points by trial and error. The lamina remains horizontal when pivoted at a point. The net gravitatioinal force acts at the point. It is the centre of gravity as shown in the figure.
When a body is supported at the centre of gravity, the sum of the torques acting on all the point masses of the rigid body becomes zero. in addition the weight is compensated by the normal reaction force exerted by the pivot. The body is in static equuilibriu. Hence it remains horizontal.