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 in a horizontal plane with an angular velocity `ω` about a vertical axis passing through one end, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a uniform rod of length `l` and mass `m` rotating about a vertical axis at one end with angular velocity `ω`. We need to find the tension in the rod at a distance `x` from the axis of rotation.

2. **Identifying the Element of the Rod**:
...