Tube \(A\) rotates about the vertical \(O\)-axis with a constant angular rate \(\dot{\theta}=\omega\) and contains a small cylindrical plug \(B\) of mass \(m\) whose radial position is controlled by the cord which passes freely through the tube and shaft and is wound around the drum of radius \(b\). Determine the tension \(T\) in the cord and the horizontal component \(F_{\theta}\) of force exerted by the tube on the plug if the constant angular rate of rotation of the drum is \(\omega_{0}\) first in the direction for case \((a)\) and second in the direction for case (b). Neglect friction.

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= B A b. wo case (a) 3 = 8 w wo case (b) +8 , T B -+r Fo