Consider a disc of mass \(m\) and radius \(R\) touching a rough wall of coefficient of friction \(\mu\) and a rough floor of coefficient of friction \(\mu\) as shown in figure. The ring has an initial angular velocity of \(\omega_0\).
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Find the time taken by the ring to come to a halt.

**Details and Assumptions**

The disc neither translates on the floor nor on the wall

\(\mu = \dfrac{1}{2} \)

\(m = 1 kg \)

\(R = 4 m\)

\(g = 10 m/s^2 \)

\(\omega_0 = 9 rad/s \)

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