Question 2 - A-Level Maths

\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4acdc4d7-01f0-496f-9390-de5f136bc5f9-2_333_551_488_836} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} A uniform piece of wire, \(A B C\), forms a semicircular arc of radius \(6 \mathrm {~cm} . O\) is the mid-point of \(A C\) (see Fig. 1). Show that the distance from \(O\) to the centre of mass of the wire is 3.82 cm , correct to 3 significant figures.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4acdc4d7-01f0-496f-9390-de5f136bc5f9-2_579_721_1178_753} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Two semicircular pieces of wire, \(A B C\) and \(A D C\), are joined together at their ends to form a circular hoop of radius 6 cm . The mass of \(A B C\) is 3 grams and the mass of \(A D C\) is 5 grams. The hoop is freely suspended from \(A\) (see Fig. 2). Calculate the angle which the diameter \(A C\) makes with the vertical, giving your answer correct to the nearest degree.