2. A right circular cylindrical component is loaded in tension as shown in the diagram below. A fixed load is imposed on the sample by a weight. A potential research sponsor would like to know how difficult it might be to detect internal cracking by monitoring displacement on the boundary of such a cylinder. In order to give her a reasonable answer (and win a grant) you decide to calculate the displacement, Au, at the point of loading when an embedded circular crack of diameter 2a is allowed to form in the center of the cylinder. Derive an expression for the change in nominal displacement, Au, as a function of crack radius, a, for a fixed load, P, assuming that the material behaves in a linear elastic manner and that the crack is small compared to the size of the sample, 2a <