$A$ small mass $m$, attached to one end of a spring with a negligible mass and an unstretched length $L$, executes vertical oscillations with angular frequency $\omega_{0}$. When the mass is rotated with an angular speed $\omega$ by holding the other end of the spring at a fixed point, the mass moves uniformly in a circular path in a horizontal plane. Then the increase in length of the spring during the rotation is

• A
  $\frac{\omega^{2} L}{\omega_{0}^{2}-\omega^{2}}$
• B
  $\frac{\omega_{0}^{2} L}{\omega^{2}-\omega_{0}^{2}}$
• C
  $\frac{\omega^{2} L}{\omega_{0}^{2}}$
• D
  $\frac{\omega_{0}^{2} L}{\omega^{2}}$