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A small ring \( P \) is threaded on a smooth wire bent in the form of a circle of radius \( a \) and center \( O \). The wire is rotating with constant angular speed \( \omega \) about a vertical diameter \( X Y \), while the ring remains at rest relative to the wire at a distance \( a / 2 \) from \( X Y \). Then \( \omega^{2} \) is equal to
\( \mathrm{P} \)
W
(1) \( \frac{2 g}{a} \)
(2) \( \frac{g}{2 a} \)
(3) \( \frac{2 g}{a \sqrt{3}} \)
(4) \( \frac{g \sqrt{3}}{2 a} \)
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