$A$ rod of mass $m$ and length $l$ is rotated about one of its ends with an angular velocity $\omega$. What is the tension in the rod at a distance $x$ from the axis of rotation?

• A
  $\frac{1}{2}m{\omega ^2}x$
• B
  $\frac{1}{2}m{\omega ^2}\frac{{{x^2}}}{l}$
• C
  $\frac{1}{2}m{\omega ^2}l\left( {1 - \frac{x}{l}} \right)$
• D
  $\frac{1}{2}\frac{{m{\omega ^2}}}{l}[{l^2} - {x^2}]$