5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3706a02d-95c6-4e7a-bf38-88b338d77892-09_270_919_267_557}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a uniform solid \(S\) formed by joining the plane faces of two solid right circular cones, of base radius \(r\), so that the centres of their bases coincide at \(O\). One cone, with vertex \(V\), has height \(4 r\) and the other cone has height \(k r\), where \(k > 4\)
- Find the distance of the centre of mass of \(S\) from \(O\).
(4)
The point \(A\) lies on the circumference of the common base of the cones. The solid is placed on a horizontal surface with VA in contact with the surface. Given that \(S\) rests in equilibrium, - find the greatest possible value of \(k\).
When \(S\) is suspended from \(A\) and hangs freely in equilibrium, \(O A\) makes an angle of \(12 ^ { \circ }\) with the downward vertical.
- Find the value of \(k\).