A particle \( P \) of mass \( m \) is attached to a vertical axis by two strings \( A P \) and \...

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A particle \( P \) of mass \( m \) is attached to a vertical axis by two strings \( A P \) and \( B P \) of length \( l \) each. The separation \( A B=l . P \) rotates around the axis with an angular velocity \( \omega \). The tensions in the two strings are \( T_{1} \) and \( T_{2} \). Choose the correct option(s).
\( \mathrm{P} \)
(1) \( T_{1}=T_{2} \)
(2) \( T_{1}=T_{2}=m \omega^{2} l \)
(3) \( T_{1}+T_{2}=2 m g \)
(4) \( B P \) will remain taut only if \( \omega \geq \sqrt{2 g / l} \)
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