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A uniform solid consists of a hemisphere of radius r and a right circular cone of base radius r and height h , fixed together so that their plane faces coincide . The solid can rest in equilibrium with any point of the curved surface of the hemisphere in contact with a horizontal plane.Find h in terms of r.

My working :

1. I find the mass of the cone and the hemisphere.

2. Centre of mass of the cone and the hemisphere

3. tabulate it and find the centre of the mass of the composite body.

Problem :

After find x bar of the composite body , i have no idea how to find h in terms of r . I do not understand what information they are giving me when they say that "The solid can rest in equilibrium with any point of the curved surface of the hemisphere in contact with a horizontal plane" .

Could anyone help me out . Thanks .