5. A particle \(P\), of mass 0.5 kg , rests on the surface of a rough horizontal table. The coefficient of friction between \(P\) and the table is \(0.5 . P\) is connected to a particle \(Q\), of mass 0.2 kg , by a light inextensible string passing through
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   a small smooth hole at a point \(O\) on the table, such that the distance \(O Q\) is \(0.4 \mathrm {~m} . Q\) moves in a horizontal circle while \(P\) remains in limiting equilibrium.
   1. Calculate the angle \(\theta\) which \(O Q\) makes with the vertical.
   2. Show that the speed of \(Q\) is \(1.33 \mathrm {~ms} ^ { - 1 }\).
   The motion is altered so that \(Q\) hangs at rest below \(O\) and \(P\) moves in a horizontal circle on the table with speed \(0.84 \mathrm {~ms} ^ { - 1 }\), at a constant distance \(r \mathrm {~m}\) from \(O\) but tending to slip away from \(O\).
2. Find the value of \(r\).