Question

A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is 

(a) smallest at the top and gradually increases down the rod 

(b) largest at the top and gradually decreases down the rod 

(c) uniform everywhere 

(d) maximum in the middle.

Answer 1

(a) smallest at the top and gradually increases down the rod

Explanation: 

For a hanged heavy uniform rod, at any cross-section, the load is only of the part of the rod which is below it. At its lowest point, the load is zero which gradually increases as we go up. Since the cross-section is the same, the stress increases as we go up. The maximum stress will be at the top and so will be the effect of elongation. Since the transverse strain is proportional to longitudinal strain, hence the diameter of the rod will be smallest at the top and gradually increase down the rod.