4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2c7ac0e1-14fd-4e50-935a-d82e7127c2f8-07_707_481_228_733}
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\caption{Figure 2}
\end{figure}
Figure 2 shows the cross-section \(A V B C\) of the solid \(S\) formed when a uniform right circular cone of base radius \(a\) and height \(a\), is removed from a uniform right circular cone of base radius \(a\) and height \(2 a\). Both cones have the same axis VCO, where \(O\) is the centre of the base of each cone.
- Show that the distance of the centre of mass of \(S\) from the vertex \(V\) is \(\frac { 5 } { 4 } a\).
The mass of \(S\) is \(M\). A particle of mass \(k M\) is attached to \(S\) at \(B\). The system is suspended by a string attached to the vertex \(V\), and hangs freely in equilibrium. Given that \(V A\) is at an angle \(45 ^ { \circ }\) to the vertical through \(V\),
- find the value of \(k\).