2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2633b149-96db-4b80-96c2-e3e6bfbee174-04_515_1282_269_331}
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\caption{Figure 1}
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A uniform rod \(A B\) has length \(2 a\) and mass \(M\). The rod is held in equilibrium in a horizontal position by two vertical light strings which are attached to the rod at \(C\) and \(D\), where \(A C = \frac { 2 } { 5 } a\) and \(D B = \frac { 3 } { 5 } a\), as shown in Figure 1.
A particle \(P\) is placed on the rod at \(B\).
The rod remains horizontal and in equilibrium.
- Find, in terms of \(M\), the largest possible mass of the particle \(P\)
Given that the mass of \(P\) is \(\frac { 1 } { 2 } M\)
- find, in terms of \(M\) and \(g\), the tension in the string that is attached to the rod at \(C\).