3.
\begin{figure}[h]
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\caption{Figure 2}
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Figure 2 shows a container in the shape of a uniform right circular conical shell of height 6r. The radius of the open circular face is \(r\). The container is suspended by two vertical strings attached to two points at opposite ends of a diameter of the open circular face. It hangs with the open circular face uppermost and axis vertical. Molten wax is poured into the container. The wax solidifies and adheres to the container, forming a uniform solid right circular cone. The depth of the wax in the container is \(2 r\). The container together with the wax forms a solid \(S\).
The mass of the container when empty is \(m\) and the mass of the wax in the container is \(3 m\).
- Find the distance of the centre of mass of the solid \(S\) from the vertex of the container.
One of the strings is now removed and the solid \(S\) hangs freely in equilibrium suspended by the remaining vertical string.
- Find the size of the angle between the axis of the container and the downward vertical.