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 kl(3/2) is the first zero of J-1/3 and k=4/3r2*√(ρg/∏Y) where r is the radius, ρ is the linear density, g is the acceleration of gravity, and Y is the Young modulus. Find l for a steel wire of radius 1 mm; for a lead wire of the same radius. What I've done so far is plug -1/3 in for p to simplify the Bessel function, and then set that equal to zero. What I really am interested in is how to derive the expression with the Bessel function, but I really don't know where to start. Any suggestions on how to tackle this? Much appreciated.