Answer
See answers.
Work Step by Step
The maximum compressive force in a column is mg, and occurs at the bottom.
For the column to buckle, its weight divided by the cross-sectional area equals the compressive strength CS of the material. The mass of the column is (density)(volume ).
$$\frac{mg}{A}=CS=\frac{\rho hAg}{A}$$
$$h=\frac{CS}{\rho g}$$
a. For steel, using data from page 245:
$$h=\frac{500\times10^6\;N/m^2}{7800\;kg/m^3 (9.80\;m/s^2)}=6500m$$
b. For granite, using data from page 245:
$$h=\frac{170\times10^6\;N/m^2}{2700\;kg/m^3 (9.80\;m/s^2)}=6400m$$
