A uniform solid cylinder of mass \(m = 2\text{ kg}\) is given and angular velocity of \( \omega = 5\text{ rad/sec} \) and is dropped from a height of \(h = 22 \text{ m}\) on a rough floor at \(t = 0 \).

It collides with the sufficiently rough ground such that its velocity in the vertical direction reduces to zero.

Find the time, \(t\) (in seconds) after which it starts pure rolling.

**Details and Assumptions**:

Coefficient of friction of ground is \(\mu = 0.2\).

Radius of cylinder is \( R = 2 \text{ m}\), \( g = 10\text{ m/s}^2\).

Initial height measured is of centre of mass of cylinder from ground.

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