A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular v...

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A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity \( \omega \) in a circular path of radius \( R \) (figure 7-E3). A smooth groove \( A B \) of length \( L(R) \) is made on the surface of the table. The groove makes an angle \( \theta \) with the radius \( O A \) of the circle in which the cabin rotates. A small particle is kept at the point \( A \) in the groove and is released to move along \( A B \). Find the time taken by the particle to reach the point \( B \).
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