Take a solid cylinder of radius \(R\) , roll it with angular velocity \(\omega_{0}\) and carefully keep it on an inclined plane having inclination \(\theta\) , and coefficient of kinetic friction \(\mu_{k}\) , such that \(\mu_{k} > \tan \theta\). Find the maximum height attained by the cylinder above the initial position in \(mm\) **to the nearest integer**

**Details and Assumptions**

- \(\omega_{0} = 50 rad s^{-1}\)
- \(R = 25cm\)
- \(\mu_{k} = \frac{1}{3}\)
- \(\tan \theta = \frac{1}{4}\)
- \(g=9.8 m/s^2\)

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