5.
\includegraphics[max width=\textwidth, alt={}, center]{6d6b6de9-ec06-4b55-8dc6-4923a3554ffa-4_1185_1059_239_416} A model tree is made by joining a uniform solid cylinder to a uniform solid cone made of the same material. The centre \(O\) of the base of the cone is also the centre of one end of the cylinder, as shown in Fig. 2. The radius of the cylinder is \(r\) and the radius of the base of the cone is \(2 r\). The height of the cone and the height of the cylinder are each \(h\). The centre of mass of the model is at the point \(G\).

1. Show that \(O G = \frac { 1 } { 14 } h\).
   (8) The model stands on a desk top with its plane face in contact with the desk top. The desk top is tilted until it makes an angle \(\alpha\) with the horizontal, where tan \(\alpha = \frac { 7 } { 26 }\). The desk top is rough enough to prevent slipping and the model is about to topple.
2. Find \(r\) in terms of \(h\).
   (4)