6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0a4e4cdd-bec4-4059-b9f7-9ce00bc34b71-20_721_958_127_495}
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\caption{Figure2}
\end{figure}
Figure 2 shows a uniform rod \(A B\) of mass \(m\) and length 4a. The end \(A\) of the rod is freely hinged to a point on a vertical wall. A particle of mass \(m\) is attached to the rod at \(B\). One end of a light inextensible string is attached to the rod at C , where \(\mathrm { AC } = 3 \mathrm { a }\). The other end of the string is attached to the wall at D , where \(\mathrm { AD } = 2 \mathrm { a }\) and D is vertically above A . The rod rests horizontally in equilibrium in a vertical plane perpendicular to the wall and the tension in the string is T .
- Show that \(\mathrm { T } = \mathrm { mg } \sqrt { } 13\).
(5)
The particle of mass \(m\) at \(B\) is removed from the rod and replaced by a particle of mass \(M\) which is attached to the rod at B . The string breaks if the tension exceeds \(2 \mathrm { mg } \sqrt { } 13\). Given that the string does not break, - show that \(M \leqslant \frac { 5 } { 2 } m\).