2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c14975b7-6afa-44ce-beab-1cba2e82b249-06_373_847_251_609}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A uniform rod of length \(28 a\) is cut into seven identical rods each of length \(4 a\). These rods are joined together to form the rigid framework \(A B C D E A\) shown in Figure 1.
All seven rods lie in the same plane.
The distance of the centre of mass of the framework from \(E D\) is \(d\).
- Show that \(d = \frac { 8 \sqrt { 3 } } { 7 } a\)
The weight of the framework is \(W\).
The framework is freely pivoted about a horizontal axis through \(C\).
The framework is held in equilibrium in a vertical plane, with \(A C\) vertical and \(A\) below \(C\), by a horizontal force that is applied to the framework at \(A\).
The force acts in the same vertical plane as the framework and has magnitude \(F\). - Find \(F\) in terms of \(W\).