A uniform heavy rod of weight W, cross sectional area a and length L is hanging from fixed support. Young modulus of the material of the rod is Y. Neglect the lateral contraction. Find the elongation of the rod.

Explanation

To find the elongation of a uniform heavy rod of weight \( W \), cross-sectional area \( A \), length \( L \), and Young's modulus \( Y \), we can follow these steps:

### Step 1: Understand the Forces Acting on the Rod
The rod is hanging from a fixed support, and its weight \( W \) acts downward. The weight creates tension in the rod, which varies along its length.

### Step 2: Define the Element of the Rod
Consider an infinitesimal element of the rod at a distance \( x \) from the top, with a small length \( dx \). The tension \( T \) in this element is due to the weight of the portion of the rod below it.

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