Elastic energy is the potential mechanical energy stored in the volume of a material when that volume is compressed or stretched. The elastic energy W corresponding to a volume R of a certain material is (q^2)R/(2EI), where q is its stress and E and I are constants. Find the elastic energy of a cylindrical volume of radius a and length l in which the stress varies directly as the distance from its axis, being zero at the axis
and q0 at the outer surface. Justify your answer by commenting on the influence of a and l on this energy.