A uniform cylinder is given an angular velocity of \( \omega = 5\text{ rad/sec}\) in clockwise direction and dropped from the height \( h = 22\text { m}\) .

It collides with the sufficiently rough ground such that its component of velocity in the vertical direction reduces to zero. And just after the impact, it starts pure rolling on the ground.

Find the minimum coefficient of friction of the rough ground required \( \min( \mu )\).

**Details and Assumptions**:

The radius of cylinder is \( R = 2\text{ m}\).

The initial height measured is from the centre of mass of cylinder from ground.

Acceleration due to gravity, \( g = 10\text{ m/s}^2 \).

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