\includegraphics{figure_1}

A uniform rod $AB$ has length $100 \text{ cm}$. Two light pans are suspended, one from each end of the rod, by two strings which are assumed to be light and inextensible. The system forms a balance with the rod resting horizontally on a smooth pivot, as shown in Fig. 1.

A particle of weight $16 \text{ N}$ is placed in the pan at $A$ and a particle of weight $5 \text{ N}$ is placed in the pan at $B$. The rod rests horizontally in equilibrium when the pivot is at the point $C$ on the rod, where $AC = 30 \text{ cm}$.

\begin{enumerate}[label=(\alph*)]
\item Find the weight of the rod. [3]
\end{enumerate}

The particle in the pan at $A$ is replaced by a particle of weight $3.5 \text{ N}$. The particle of weight $5 \text{ N}$ remains in the pan at $B$. The rod now rests horizontally in equilibrium when the pivot is moved to the point $D$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the distance $AD$. [4]
\item Explain briefly where the assumption that the strings are light has been used in your answer to part (a). [1]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2002 Q3 [8]}}