Rope in a circular tube

A rope of mass MM having length πr\pi r is placed in a vertical circular tube centered at the origin. The mean radius of the tube is r=20π3 mr = \SI{\dfrac{20}{\pi^{3}}}{\meter}. The width of the tube is such that it just fits the rope.

The rope is slightly pulled from one end and released to oscillate. If the tube is frictionless, find the time period (in seconds) of the small oscillations. (\big(Take acceleration due to gravity g=10 m/s2.)g=\SI[per-mode=symbol]{10}{\meter\per\second\squared}.\big)

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