2 A uniform solid cone has height 38 cm .
- Write down the distance of the centre of mass of the cone from its base.
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The cone is placed with its axis vertical on a rough horizontal plane. The plane is slowly tilted, and the cone remains in equilibrium until the angle of inclination of the plane reaches \(31 ^ { \circ }\) (see diagram), when the cone topples. - Find the radius of the cone.
- Show that \(\mu \geqslant 0.601\), correct to 3 significant figures, where \(\mu\) is the coefficient of friction between the cone and the plane.