$\backslash$table$[[$Material$,\backslash$table$[[$Young$\text{'}$s modulus,$],[$E$,($GPa$)]],$Crystal structure,Cost$],[$Mild steel,$210,$Body$-$centred cubic,Low$],[\backslash$table$[[301$ Stainless$],[$steel$,$ annealed$]],193,$Face$-$centred cubic,High$],[$Diamond$,1200,$Diamond cubic,Very high$]]$

$($a$)$ Which material from the table would have the

$[1]$

highest stiffness, and Why its Young's Modulus is significantly higher compared to the other two materials?

$($b$)$ You are required to select a material for the

$[2]$ following application:

A rod $($vertical$,$ as shown, fixed at the top$)$ suspends a mass of $20$ kg $.$ Which of the above materials, if selected for the rod, will lengthen the least under this load? Why?

$($c$)$ Would you select this material? Why$/$why not?

$($d$)$ Which of the above materials, would you expect to be the most ductile? Why?

$($e$)$ If mild steel is selected for the rod, how much will the rod extend under the load mass while remaining within the elastic deformation range? Please provide the result rounded to one decimal place in micrometers?

$($f$)$ The first two materials are alloys. What is the approximate carbon content of each alloy? You

$[4]$