A ballet dancer is rotating at angular velocity \( \omega \) on smo...

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A ballet dancer is rotating at angular velocity \( \omega \) on smooth horizontal floor. The
\( \mathrm{P} \) ballet dancer folds his body close to his axis

W of rotation by which his radius of gyration decreases by \( 1 / 4^{\text {th }} \) of his initial radius of gyration, his final angular velocity is
(1) \( \frac{3}{4} \)
(2) \( \frac{9}{4} \)
(3) \( \frac{9}{16} \)
(4) \( \frac{16}{9} \)
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