8 A shape, \(S\), is formed by attaching a particle of mass \(2 m \mathrm {~kg}\) to the vertex of a uniform solid cone of mass \(8 m \mathrm {~kg}\). The height of the cone is \(h \mathrm {~m}\) and the radius of the base of the cone is 1.1 m .
- Explain why the centre of mass of \(S\) must lie on the central axis of the cone.
Two strings are attached to \(S\), one at the vertex of the cone and one at \(A\) which is a point on the edge of the base of \(S\). The other ends of the strings are attached to a horizontal ceiling in such a way that the strings are both vertical. The string attached to \(S\) at \(A\) is inextensible and has length 1.6 m . The string attached to \(S\) at the vertex is elastic with modulus of elasticity 8 mgN .
Shape \(S\) is in equilibrium with its axis horizontal (see diagram).
\includegraphics[max width=\textwidth, alt={}, center]{05b479a4-4087-4332-924b-43b1aedbb4f2-6_654_1541_879_244} - Determine the natural length of the elastic string.