The maximum height of a cylindrical column is limited by the compressive strength of the material; if the compressive stress at the bottom were to exceed the compressive strength of the material, the column would be crushed under its own weight.
(a) For a cylindrical column of height h and radius r, made of material of density ( calculate the compressive stress at the bottom of the column.
(b) Since the answer to part (a) is independent of the radius r, there is an absolute limit to the height of a cylindrical column, regardless of how wide it is. For marble, which has a density of 2.7 × 103 kg / m3 and a compressive strength of 2.0 × 108 Pa, find the maximum height of a cylindrical column.
(c) Is this limit a practical concern in the construction of marble columns? Might it limit the height of a beanstalk?