5. \begin{figure}[h] \end{figure} Figure 1 shows a triangular lamina \(A B C\). The coordinates of \(A , B\) and \(C\) are ( 0,4 ), ( 9,0 ) and \(( 0 , - 4 )\) respectively. Particles of mass \(4 m , 6 m\) and \(2 m\) are attached at \(A , B\) and \(C\) respectively.

1. Calculate the coordinates of the centre of mass of the three particles, without the lamina. The lamina \(A B C\) is uniform and of mass \(k m\). The centre of mass of the combined system consisting of the three particles and the lamina has coordinates \(( 4 , \lambda )\).
2. Show that \(k = 6\).
3. Calculate the value of \(\lambda\). The combined system is freely suspended from \(O\) and hangs at rest.
4. Calculate, in degrees to one decimal place, the angle between \(A C\) and the vertical.
   (3) \section*{6.} \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{97fbfac6-6c1c-4a5c-ab5d-adc3193bfedc-5_693_556_338_712}
   \end{figure} A ladder \(A B\), of weight \(W\) and length \(4 a\), has one end \(A\) on rough horizontal ground. The coefficient of friction between the ladder and the ground is \(\mu\). The other end \(B\) rests against a smooth vertical wall. The ladder makes an angle \(\theta\) with the horizontal, where \(\tan \theta = 2\). A load of weight \(4 W\) is placed at the point \(C\) on the ladder, where \(A C = 3 a\), as shown in Figure 2. The ladder is modelled as a uniform rod which is in a vertical plane perpendicular to the wall. The load is modelled as a particle. Given that the system is in limiting equilibrium,