7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f5449ec3-ead0-464f-9d03-f225cd21bca6-5_536_848_191_397}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
Figure 3 shows a hotel 'key' consisting of a rectangle \(O A B D\), where \(O A = 8 \mathrm {~cm}\) and \(O D = 4 \mathrm {~cm}\), joined to a semicircle whose diameter \(B C\) is 4 cm long. The thickness of the key is negligible and the same material is used throughout.
The key is modelled as a uniform lamina.
Using this model,
- find, correct to 3 significant figures, the distance of the centre of mass from
- OD ,
- \(O A\).
A small circular hole of negligible diameter is made at the mid-point of \(B C\) so that the key can be hung on a smooth peg. When the key is freely suspended from the peg,
- find, correct to 3 significant figures, the acute angle made by \(O A\) with the vertical.