5 A vertical hollow cylinder of radius 0.4 m is rotating about its axis. A particle \(P\) is in contact with the rough inner surface of the cylinder. The cylinder and \(P\) rotate with the same constant angular speed. The coefficient of friction between \(P\) and the cylinder is \(\mu\).

1. Given that the angular speed of the cylinder is \(7 \mathrm { rad } \mathrm { s } ^ { - 1 }\) and \(P\) is on the point of moving downwards, find the value of \(\mu\). The particle is now attached to one end of a light inextensible string of length 0.5 m . The other end is fixed to a point \(A\) on the axis of the cylinder (see diagram).
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2. Find the angular speed for which the contact force between \(P\) and the cylinder becomes zero.