If X is the circumferential (hoop) stress and Y is the longitudinal stress in a thin-walled cylindrical pressure vessel subjected to internal pressure, then which of the following relations is TRUE?

When a bar of length l and uniform cross-section is rigidly fixed at the upper end and hangs freely, the total elongation produced in the bar due to its own weight is given by (where w = weight per unit volume and E = Modulus of Elasticity):

The hoop stress set up in a thin cylinder subjected to internal fluid pressure is: