$3.$ You are provided the data below for S$-$N curve of $3$ different metals. A cylindirical rod is to be used in a mechanism that will be employed in an aircraft wing. The rod has a length of $200$ cm and a radius of $10$ mm $.$ This rod bears cyclic loads of $\backslash (\backslash$pm $100\backslash$mathrm$\{$kN$\}\backslash )$ and we want it to last at least $\backslash (10^\{5\}\backslash )$ cycles. We also want it to be as light as possible as we use several of them in one wing.

a$)$ Looking at the diagram above, can you tell if aluminum or steel is more suitable to fabricate this rod from?

b$)$ If you found that steel is more suitable to endure $\backslash (10^\{5\}\backslash )$ cycles, would doubling the radius of the rod help to use aluminum instead for the purpose of weight shedding? $($Density of Al: $\backslash (2\mathrm{.}7\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$cm$\}3\backslash ),$ density of steel: $\backslash (7\mathrm{.}87\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$cm$\}3\backslash )).$