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

The correct option is A

Smallest at the top and gradually increases down the rod

Let us divide the whole rod into very small equal parts each of length dx. Any small length element will be pulled by a force due the weight of all length elements below it. Now the uppermost part of the rod will be under maximum tension force and thus will undergo maximum extension comparatively.

Hence by repeating the process, we will obtain a rod thinnest at the top and thickest at the bottom.

Hence (a)