A thin cylinder $75$ mm internal diameter, $250$ mm long with walls $1\mathrm{.}5$ mm thick is subjected to an internal pressure of $7M\frac{N}{m^2}.$ Determine the change in internal diameter and the change in length. If in addition to the internal pressure, the cylinder is subjected to a torque of $200$ Nm $.$ Find the magnitude and nature of the principal stresses set up in the cylinder. $E=200$GPa&$v=0\mathrm{.}3$

$(20$ marks$)$