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A disc of radius R is spun to an angular...

A disc of radius `R` is spun to an angular speed `omega_(0)` about its axis and then imparted a horizontal velocity of magnitude `(omega_(0)R)/(4)` (at `t=0`) with its plane remaining vertical. The coefficient of friction between the disc and the plane is `mu`. The sense of rotation and direction of its linear speed are shown in the figure. The disc returns to its initial point in time `T=(25)/(6k mug)omega_(0)R`. Find the value of `k`.

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