An object is formed by removing a solid hemisphere of radius \(2r\) from a uniform solid cone of radius \(3r\) and semi-vertical angle \(\theta\), where \(\tan\theta=\frac12\). The axes of symmetry coincide, and the cone and hemisphere have their bases in the same plane.

(a) Find, in terms of \(r\), the distance of the centre of mass of the object from its base.

(b) The object is placed with its circular base on a rough plane inclined at angle \(\alpha\). The object is on the point of toppling. Find \(\alpha\).