In this presentation we will only be discussing the elastic behavior of materials--what will happen when they stretched or squished non-destructively ("bowed"), and can still return to their original state afterwards. As for "bent" and "broken," we'll defer that discussion as our focus will be on avoiding permanent distortion or damage to materials.
Tension is when you stretch something, like these bridge suspension cables.
Compression is when you squish something, like the stones near the bottom of this stack.
For the different lengths of cable, which are stretched by the least amount (say, measured in cm) from their original lengths: the shorter lengths of cable, or the longer lengths of cable?
Let's rewrite Hooke's law in terms of ∆L and L, as these are different for the short and long lengths of cable, and have cross-sectional area A, Young's modulus Y, and the tension F all on the other side of the equation, as these quantities are all the same for both short and long lengths of cable:
(∆L/L) = F/(A·Y).
So the right-hand side of this equation is the same for both the short and long lengths of cable:
(∆Lshort/Lshort) = F/(A·Y),
(∆Llong/Llong) = F/(A·Y),
so we can set the left-hand sides of both these equations equal to each other:
(∆Lshort/Lshort) = (∆Llong/Llong).
Since Lshort < Llong, then for the equality to hold, ∆Lshort < ∆Llong, and thus the shorter cable will stretch by a smaller amount than the longer cable.
For the different cross-sectional area columns, which support the least amount of force: the narrower cross-sectional area columns, or the wider cross-sectional area columns?