- A uniform solid right circular cone \(C\) has base radius \(r\), height \(H\) and vertex \(V\). A uniform solid \(S\), shown in Figure 3, is formed by removing from \(C\) a uniform solid right circular cone of height \(h ( h < H )\) that has the same base and axis of symmetry as \(C\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dceb2432-117c-40fe-bf3d-782beeb42e41-08_725_1152_422_461}
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\caption{Figure 3}
\end{figure}
- Show that the distance of the centre of mass of \(S\) from \(V\) is
$$\frac { 1 } { 4 } ( 3 H - h )$$
The solid \(S\) is suspended by two vertical light strings. The first string is attached to \(S\) at \(V\) and the second string is attached to \(S\) at a point on the circumference of the circular base of \(S\).
The solid \(S\) hangs freely in equilibrium with its axis of symmetry horizontal.
The tension in the first string is \(T _ { 1 }\) and the tension in the second string is \(T _ { 2 }\) - Find \(\frac { T _ { 1 } } { T _ { 2 } }\), giving your answer in terms of \(H\) and \(h\), in its simplest form.