Chapter 12.18, Problem 11P

A straight wire clamped vertically at its lower end stands vertically if it is short, but bends under its own weight if it is long. It can be shown that the greatest length for vertical equilibrium is $l$, where $k{l}^{3/2}$ is the first zero of $J_{-1/3}$ and $k=\frac{4}{3r^2}\sqrt{\frac{\rho g}{\pi Y}},$ $r=$ radius of the wire, $\rho =$ linear density, $g=$ acceleration of gravity, $Y=$ Young’s modulus. Find $l$ for a steel wire of radius1 mm; for a lead wire of the same radius.