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A uniform solid cone of height 1.2 m and semi-vertical angle $\theta ^ { \circ }$ is divided into two parts by a cut parallel to and 0.4 m from the circular base. The upper conical part, $C$, has weight 16 N , and the lower part, $L$, has weight 38 N . The two parts of the solid rest in equilibrium with the larger plane face of $L$ on a horizontal surface and the smaller plane face of $L$ covered by the base of $C$ (see diagram).\\
(i) Calculate the distance of the centre of mass of $L$ from its larger plane face.

An increasing horizontal force is applied to the vertex of $C$. Equilibrium is broken when the magnitude of this force first exceeds 4 N , and $C$ begins to slide on $L$.\\
(ii) By considering the forces on $C$,\\
(a) find the coefficient of friction between $C$ and $L$,\\
(b) show that $\theta > 14.0$, correct to 3 significant figures.\\
$C$ is removed and $L$ is placed with its curved surface on the horizontal surface.\\
(iii) Given that $L$ is on the point of toppling, calculate $\theta$.

\hfill \mbox{\textit{CAIE M2 2013 Q6}}