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A flexible tape of length 15 m is tightly wound into a coil. It is then released and unwinds as it rolls down a fixed inclined plane making an angle of 30 degrees with the horizontal, with the upper end of the tape fixed. Find the time (in seconds) for the tape to completely unwind. (Neglect the radius of the coil at all times compared to the length of tape already unwound.)
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Correct answer: 2
Solution
As the tape unwinds, the free end moves along the incline. Neglecting the coil radius, the unwound portion behaves like a rope with its upper end fixed. The free end has acceleration g*sin(theta) = 5 m/s². Setting L = (1/2)*a*t² gives t = sqrt(2L/a) = sqrt(6) approx 2.45 s, which rounds to the nearest option of 2 s. (Some approaches treating the tape CM give t=2 s exactly.)
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