3.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{7ae16b00-d388-4c1b-a195-c785a3900548-04_648_732_301_612}
\end{figure}
Figure 1 shows a template \(T\) made by removing a circular disc, of centre \(X\) and radius 8 cm , from a uniform circular lamina, of centre \(O\) and radius 24 cm . The point \(X\) lies on the diameter \(A O B\) of the lamina and \(A X = 16 \mathrm {~cm}\). The centre of mass of \(T\) is at the point \(G\).
- Find \(A G\).
The template \(T\) is free to rotate about a smooth fixed horizontal axis, perpendicular to the plane of \(T\), which passes through the mid-point of \(O B\). A small stud of mass \(\frac { 1 } { 4 } m\) is fixed at \(B\), and \(T\) and the stud are in equilibrium with \(A B\) horizontal. Modelling the stud as a particle,
- find the mass of \(T\) in terms of \(m\).