A heavy uniform rod hangs vertically from a fixed support and undergoes stretching due to its own weight. The diameter of this rod is

Step-by-step solution

Let the length of the rod be L , its total weight be W , and its initial cross-sectional area be A . The tension T at a distance x from the bottom of the hanging rod is equal to the weight of the rod below that cross-section, given by T = W x L . The longitudinal stress at this point is = T A = W x A L . The stress is maximum at the top support ( x = L ) and zero at the free bottom end ( x = 0 ). Longitudinal strain is directly proportional to longitudinal stress. According to Poisson's ratio, a longitudinal extens