4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a687d17-ec7e-463f-84dd-605f5c230db1-12_442_506_251_721}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
A uniform right solid cone \(C\) has diameter \(6 a\) and height \(8 a\), as shown in Figure 3.
The solid \(S\) is formed by removing a cone of height \(4 a\) from the top of \(C\) and then removing an identical, inverted cone. The vertex of the removed cone is at the point \(O\) in the centre of the base of \(C\), as shown in Figure 4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a687d17-ec7e-463f-84dd-605f5c230db1-12_236_502_1126_721}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
- Find the distance of the centre of mass of \(S\) from \(O\).
(5)
The point \(A\) lies on the circumference of the base of \(S\) and the point \(B\) lies on the circumference of the top of \(S\). The points \(O\), \(A\) and \(B\) all lie in the same vertical plane, as shown in Figure 5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a687d17-ec7e-463f-84dd-605f5c230db1-12_248_449_1845_749}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
The solid \(S\) is freely suspended from the point \(B\) and hangs in equilibrium. - Find the size of the angle that \(A B\) makes with the downward vertical.