A thin uniform copper rod of length l and mass m rotates uniformly with an angular velocity `omega` in a horizontal plane about a vertical axis passing through one of its ends. Determine the tension in the rod as a function of the distance r from the rotation axis. Find the elongation of the rod.

Explanation

To solve the problem of determining the tension in a rotating copper rod and finding its elongation, we can follow these steps:

### Step 1: Understanding the System
We have a thin uniform copper rod of length \( l \) and mass \( m \) rotating with an angular velocity \( \omega \) about a vertical axis through one of its ends. We need to find the tension \( T \) in the rod as a function of the distance \( r \) from the rotation axis.

### Step 2: Consider a Small Element of the Rod
Let's consider a small element of the rod at a distance \( r \) from the rotation axis with a length \( dr \). The tension at this point is \( T \), and at the end of the small element, it is \( T + dT \).

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