A small ball of mass \( 1 \mathrm{~kg} \) is kept in circular path of radius \( 1 \mathrm{~m} \) inside a concentric smooth horizontal fixed casing of radius \( R \). Angular speed of the ball in the circular motion is \( 1 \mathrm{rad} \mathrm{s}^{-1} \). At a certain moment the string, which kept the ball in the circular path breaks and the ball goes off tangentially to the wall of rigid casing and bounces off elastically and again hits the casing and bounces off. This way, the ball traces a regular hexagon. Consider all the collisions to be elastic.
Total time between the first collision and the seventh collision will
(1) \( \frac{\sqrt{4}}{3} \mathrm{~s} \)
(2) \( 4 \sqrt{3} \mathrm{~s} \)
(3) \( 3 \sqrt{3} \mathrm{~s} \)
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