A helical coil spring with D$=50$mm and d$=5\mathrm{.}5$mm is wound with a pitch of $10$ mm to a

free length of $95\mathrm{.}5$ mm $.$ The ends of the spring are plain and ground. The material is ASTM

A$227$ hard$-$drawn wire.

$($a$)$ If the spring is compressed solid, would you expect it to return to its original free

length when the force is removed?

$($b$)$ Would the spring buckle during compression?