The end gear connected to the shaft is subjected to the loading shown. If the bearings at \(A\) and \(B\) exert only \(y\) and \(z\) components of force on the shaft, determine the equilibrium torque \(T\) at gear \(C\) and then determine the smallest diameter of the shaft to the nearest millimeter that will support the loading. Use the maximum shear stress theory of failure with \(\tau_{\text {allow }}=60 \mathrm{MPa}\).

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x N 250 mm C 50 mm 100 mm T 75 mm 150 mm 100 mm F = 1.5 kN B