A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled with water upto a depth of $$2$$m and suspended along with its upper rim. The density of water is $$1000$$kg/m³ and acceleration due to gravity is $$10$$ m/s². The self weight of the cylinder is negligible. The formula for hoop stress in a thin walled cylinder can be used at all points along the height of the cylindrical container.

If the Young's modulus and Poisson's ratio of the container material are $$100$$GPa and $$0.3$$, respectively. The axial strain in the cylinder wall at mid height is

A thin cylinder of $$100$$mm internal diameter and $$5$$mm thickness is subjected to an internal pressure of $$10$$ MPa and a torque of $$2000$$ Nm. Calculate the magnitudes of the principal stresses.