The centre of gravity
The point where the three lines met in the last activity has a name: the centre of gravity.
Centre of gravity
The centre of gravity is the single point at which the whole weight of a body can be taken to act.
Weight acts through the centre of gravity
So the weight W of the lamina acts along the vertical line through its centre of gravity. However large a body is, when its weight is being considered it can be treated as one force hanging at one point.
Why does it hang still?
A lamina hung from a single point comes to rest only when the point it hangs from and its centre of gravity lie on the same vertical line. If they did not, the weight and the tension would not be along one line — recall the third condition of section 12.2 — and the body would turn.
That is why the activity works
On every occasion the vertical line through the thread must pass through the centre of gravity. So marking just two such lines is enough to find it; the third is a check.