A wire of length l and radius r has a weight W and the Young's modulus of elasticity Y. it is suspended vertically from a fixed point. Calculate the increase in length of wire porduced due to its own weight.

Explanation

To solve the problem of calculating the increase in length of a wire suspended vertically due to its own weight, we can follow these steps:

### Step 1: Understand the Problem
We have a wire of length \( L \), radius \( r \), weight \( W \), and Young's modulus \( Y \). The wire is suspended vertically, and we need to find the increase in length caused by its own weight.

### Step 2: Define the Variables
- Let \( dx \) be an infinitesimal length of the wire at a distance \( x \) from the bottom.
- The weight of the wire below this element \( dx \) will exert a force on it.
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