Problem $5(15$ pts$)$

A column of rectangular cross section $(2in.$ by $3$ in $.)$ and length $50$ in $.,$ is shown below. Young's modulus is $E=10{10}^6$ psi.

a$)$ Determine the critical buckling load.

b$)$ The original column is to be replaced with one that has a circular cross section, of the same length and the same material.

If the critical buckling load is the same as in part a$),$ determine the required radius of the new column.

Will the new column weigh more or less $($justify your answer with a calculation$).$