MathDB

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?

Problem Statement