5 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 \(\frac { 4 } { 3 } \pi r ^ { 3 }\).)

1. Show that the distance of the centre of mass of the solid from \(O\) is 0.09 m .
2. 
   \includegraphics[max width=\textwidth, alt={}, center]{941c0c81-a74f-49c0-acb7-1c23266fc2c8-03_636_1036_982_593} The solid is placed with the curved surface of the hemisphere on a rough horizontal surface and the axis inclined at \(45 ^ { \circ }\) 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
   (a) the mass of the solid,
   (b) the set of possible values of the coefficient of friction between the surface and the solid.