$(5$ points$)$ The figures below depict hypothetical room$-$temperature random polycrystalline grain structures $($at the same magnification$)$ for the same single$-$component metal. Which of these structures is expected to provide the lowest yield strength?

$($v$)$

$($c$)$

$($b$)$

$($d$)$

$(3$ points$)$ When a solid containing a crack is under a tensile loading, a high stress concentration occurs at the crack tip if

a$.$ The load is applied parallel to the crack length

b$.$ The load is applied perpendicular to the crack length

$(5$ points$)$ What is the metallurgical driving force for the formation of spheroidite of a carbon steel $($e$.$g$.$ a eutectoid steel$)?$

a$.$ The diffusion of C atoms

b$.$ The high ductility of spheroidite steels

c$.$ The net reduction in ferrite$-$cementite phase boundary area