Consider a cylindrical cable with a hanging weight suspended from it$.$ Part $($a$)$

When the mass is removed, the length of the cable is found to be l$0=4\mathrm{.}61$ m$.$ After the mass is added, the length is remeasured and found to be l$1=5\mathrm{.}4$ m$.$ Determine Young's Modulus Y in N$/$m$2$ for the steel cable if the weight has a mass m $=45$ kg and the cable has a radius r $=0\mathrm{.}045$ m$.$

$$ Part $($b$)$

If we were to double the radius of the wire and re$-$suspend the weight, which of the following would be correct.

$$ Part $($c$)$

If this cable is pulled down a distance d in m from its equilibrium position it acts like a spring when released. Write an expression determining the spring constant k of this material using the cable$-$specific variables Y $,$ l$1,$ l$0,$ and r provided in part A$.$