3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a7901165-1679-4d30-9444-0c27020e32ea-08_547_410_246_829}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
The uniform lamina \(A B C D E F G H I J\) is shown in Figure 3.
The lamina has \(A J = 8 a , A B = 5 a\) and \(B C = D E = E F = F G = G H = H I = I J = 2 a\).
All the corners are right angles.
- Show that the distance of the centre of mass of the lamina from \(A J\) is \(\frac { 49 } { 26 } a\)
A light inextensible rope is attached to the lamina at \(A\) and another light inextensible rope is attached to the lamina at \(B\). The lamina hangs in equilibrium with both ropes vertical and \(A B\) horizontal. The weight of the lamina is \(W\).
- Find, in terms of \(W\), the tension in the rope attached to the lamina at \(B\).
The rope attached to \(B\) breaks and subsequently the lamina hangs freely in equilibrium, suspended from \(A\).
- Find the size of the angle between \(A J\) and the downward vertical.