A stell rod of length 2l corss sectional area A and mass M is set rotating in a horizotnal plane about an axis passing through its cnetre and perpendicular to its length with constant angular velcoty `omega.` If Y is the Young's modulus for steel, find the extension in the lenght of the rod. (Assume the rod is uniform.)

Explanation

To find the extension in the length of a rotating steel rod, we can follow these steps:

### Step 1: Understand the setup
We have a steel rod of length \(2l\), cross-sectional area \(A\), and mass \(M\) rotating about an axis through its center with a constant angular velocity \(\omega\). The rod is uniform, meaning its mass is evenly distributed.

### Step 2: Determine the forces acting on the rod
When the rod rotates, each segment of the rod experiences a centrifugal force due to the rotation. The centrifugal force \(F\) acting on a small mass element \(dm\) located at a distance \(r\) from the axis of rotation is given by:
\[
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