A homogeneous solid body is made by joining a base of a circular cylinder of height h and radius r, and the base of a hemisphere of radius r. This body is placed with the hemispherical end on a horizontal table, with the axis of the cylinder in a vertical position, and then slightly oscillated. It is intuitively evident that if r is large as compared to h, the equilibrium will be stable; but if r is small compared to h, the equilibrium will be unstable. What is the critical value of the ratio r\slash h which enables the body to rest in neutral equilibrium in any position? Putnamratiohemispherescylinder