A close$-$coiled helical spring has $100$ mm coil diameter and is made of steel wire having a diameter of $30$

mm with $20$ complete turns. It is used to arrest a moving mass of $1\mathrm{.}0$ kg having maximum compression of $50$

mm $.$ Find the maximum velocity of the moving mass that can be arrested with the spring. At that instant, find

the maximum theoretical stress that is developed within the spring. Assume $G=200$GPa. Assume that

throughout the process, total energy remnins constant. $[50\mathrm{.}31$ m$/$s$,719$ MPa $]$