Problem $4.$ A cable of cross$-$sectional area A and material density $$ is suspended over a fixed span $L.$ The maximum allowable sag $$ is specified, and the tensile stress in the cable must not exceed $0\mathrm{.}8$ of the yield stress, ${}_y.$ It may be assumed that the sag is small compared to the span, in which case the tension in the cable is given by $T=\frac{w{L}^2}{8}$ where $w$ is the weight per unit length. Show that:

a$)$ The design places a lower limit on the specific strength of the material used for the cable

b$)$ Looking at the answer of a$),$ how much it depends on the cross$-$sectional area?