2\\
\includegraphics[max width=\textwidth, alt={}, center]{7e0f600a-18f1-458b-8549-27fca592b19c-2_515_1065_861_541}

Two uniform rods $A B$ and $B C$, each of length 2 m , are freely jointed at $B$. The weights of the rods are $W \mathrm {~N}$ and 50 N respectively. The end $A$ of $A B$ is hinged at a fixed point. The rods $A B$ and $B C$ make angles $\tan ^ { - 1 } \left( \frac { 3 } { 4 } \right)$ and $\beta$ respectively with the downward vertical, and are held in equilibrium in a vertical plane by a horizontal force of magnitude 75 N acting at $C$ (see diagram).\\
(i) By taking moments about $B$ for $B C$, show that $\tan \beta = 3$.\\
(ii) Write down the horizontal and vertical components of the force acting on $A B$ at $B$.\\
(iii) Find the value of $W$.

\hfill \mbox{\textit{OCR M3 2008 Q2 [9]}}