2 A uniform solid cylinder of height 12 cm and radius \(r \mathrm {~cm}\) is in equilibrium on a rough inclined plane with one of its circular faces in contact with the plane.
- The cylinder is on the point of toppling when the angle of inclination of the plane to the horizontal is \(21 ^ { \circ }\). Find \(r\).
The cylinder is now placed on a different inclined plane with one of its circular faces in contact with the plane. This plane is also inclined at \(21 ^ { \circ }\) to the horizontal. The coefficient of friction between this plane and the cylinder is \(\mu\).
- The cylinder slides down this plane but does not topple. Find an inequality for \(\mu\).