A uniform rod of mass `m` and length `l` rotates in a horizontal plane with an angular velocity `omega` about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is

Options

A. `(1)/(2)momega^(2)x`
B. `(1)/(2)momega^(2)(1-(x^(2))/(l))`
C. `(1)/(2)momega^(2)l(1-(x^(2))/(l^(2)))`
D. `(1)/(2)momega^(2)l[1-(x)/(l)]`

Explanation

To find the tension in a uniform rod of mass \( m \) and length \( l \) rotating about a vertical axis with an angular velocity \( \omega \), we can follow these steps:

### Step 1: Understand the System
We have a uniform rod of length \( l \) and mass \( m \) rotating about a vertical axis at one end. The tension in the rod varies along its length due to the centripetal force required for circular motion.

### Step 2: Define the Variables
Let:
- \( x \) = distance from the axis of rotation to the point where we want to find the tension.
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