\includegraphics{figure_2}

A uniform rigid rod $AB$ of length $1.2\,\text{m}$ and weight $8\,\text{N}$ has a particle of weight $2\,\text{N}$ attached at the end $B$. The end $A$ of the rod is freely hinged to a fixed point. One end of a light elastic string of natural length $0.8\,\text{m}$ and modulus of elasticity $20\,\text{N}$ is attached to the hinge. The string passes over a small smooth pulley $P$ fixed $0.8\,\text{m}$ vertically above the hinge. The other end of the string is attached to a small light smooth ring $R$ which can slide on the rod. The system is in equilibrium with the rod inclined at an angle $\theta°$ to the vertical (see diagram).

\begin{enumerate}[label=(\roman*)]
\item Show that the tension in the string is $20\sin\theta\,\text{N}$. [1]
\item Explain why the part of the string attached to the ring is perpendicular to the rod. [1]
\item Find $\theta$. [3]
\end{enumerate}

\hfill \mbox{\textit{CAIE M2 2015 Q2 [5]}}