8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{278c8424-38aa-48c2-bc82-af4be9234f71-13_259_1367_228_294}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
A uniform rod \(A B\) has length 2 m and mass 50 kg . The rod is in equilibrium in a horizontal position, resting on two smooth supports at \(C\) and \(D\), where \(A C = 0.2\) metres and \(D B = x\) metres, as shown in Figure 5. Given that the magnitude of the reaction on the rod at \(D\) is twice the magnitude of the reaction on the rod at \(C\),
- find the value of \(x\).
The support at \(D\) is now moved to the point \(E\) on the rod, where \(E B = 0.4\) metres. A particle of mass \(m \mathrm {~kg}\) is placed on the rod at \(B\), and the rod remains in equilibrium in a horizontal position. Given that the magnitude of the reaction on the rod at \(E\) is four times the magnitude of the reaction on the rod at \(C\),
- find the value of \(m\).
\includegraphics[max width=\textwidth, alt={}, center]{278c8424-38aa-48c2-bc82-af4be9234f71-14_77_74_2480_1836}