P 288 ne 2010 8 A uniform solid is made of a hemisphere with centre O and radius 0.6 m, and a cylinder of radius 0.6 m and height 0.6 m. The plane face of the hemisphere and a plane face of the cylinder coincide. (The formula for the volume of a sphere is nr) i Show that the distance of the centre of mass of the solid from O is 0.09 m. ii The solid is placed with the curved surface of the hemisphere on a rough horizontal surface and the axis inclined at 45 to the horizontal. The equilibrium of the solid is maintained by a horizontal force of 2 N applied to the highest point on the circumference of its plane face (see diagram). Calculate the mass of the solid, a b the set of possible values of the coefficient of friction between the surface and the solid. 0.6 m, 0.6m 0 45 2N OOCR, GCE Mathematics, Paper 4729, January 2011