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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
\( \mathrm{P} \) 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 this rotation is
[WB-JEE 2013]
(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) \( \frac{\omega_{0}^{2} L}{\omega^{2}} \)
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