A rocket motor case is fabricated from a Cr$-$Mo low alloy steel of proof stress $1200$ MPa $,$ in the form a long cylinder of diameter $0\mathrm{.}5$ m and wall thickness $2\mathrm{.}5$ mm $.$ If the design pressure at the highest thrust is $8$ MPa $,$ calculate the largest crack size that could be tolerated in the rocket motor case, without the risk of failure at blast$-$off. Critical CTOD measured in a small test piece is $50m$ and Young's modulus is $200$ GPa $.($assume the plane stress is valid as the section thickness is small$)$