A spinning cylinder with angular velocity \(\omega_{o}\) of Mass \(M\) and radius \(R\) is lowered on a rough fixed wedge of angle \(30^{o}\) with the horizontal and coefficient of friction \(\mu=\frac{1}{\sqrt{3}}\). The cylinder is released at a height of \(3R\) from horizontal. Find the total time taken by the cylinder to reach the bottom of the incline in \(seconds\)

Take \(R=3.6~m\), \(g=10~m/s^{2}\) and \(\omega_{o}=17~rad/s\)

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