6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f180f5f0-43c5-4365-b0d8-7284220b481e-20_593_745_246_667}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
A uniform \(\operatorname { rod } A B\) has length \(8 a\) and weight \(W\).
The end \(A\) of the rod is freely hinged to a fixed point on a vertical wall.
A particle of weight \(\frac { 1 } { 4 } W\) is attached to the rod at \(B\).
A light inelastic string of length \(5 a\) has one end attached to the rod at the point \(C\), where \(A C = 5 a\).
The other end of the string is attached to the wall at the point \(D\), where \(D\) is above \(A\) and \(A D = 5 a\), as shown in Figure 4.
The rod rests in equilibrium.
The tension in the string is \(T\).
- Show that \(T = \frac { 6 } { 5 } \mathrm {~W}\)
- Find, in terms of \(W\), the magnitude of the force exerted on the rod by the hinge at \(A\).