6
\(A B C\) is a uniform lamina in the form of a triangle with \(A B = 0.3 \mathrm {~m} , B C = 0.6 \mathrm {~m}\) and a right angle at \(B\) (see diagram).
- State the distances of the centre of mass of the lamina from \(A B\) and from \(B C\).
Distance from \(A B\)
Distance from \(B C\) \(\_\_\_\_\)
The lamina is freely suspended at \(B\) and hangs in equilibrium. - Find the angle between \(A B\) and the horizontal.
A force of magnitude 12 N is applied along the edge \(A C\) of the lamina in the direction from \(A\) towards \(C\). The lamina, still suspended at \(B\), is now in equilibrium with \(A B\) vertical. - Calculate the weight of the lamina.