QUESTION 2: [15 Marks] a) The clutch system shown in Figure 1 is used to transmit torque through a 3- mm-thick oil film with dynamic viscosity 0.38 N s/m² between two identical 30-cm-diameter disks. When the driving shaft rotates at a speed of 1450 rpm, the driven shaft is observed to rotate at 1398 rpm. Assuming a linear velocity profile for the oil film, determine the transmitted torque. [8] . Driving shaft Driven shaft 30 cm 3 mm SAE 30W oil Figure 1: Transmit torque through a 3-mm-thick oil film b) A 150 mm diameter vertical cylinder rotates concentrically inside another cylinder of diameter 15.10 cm. Both cylinders are 250 mm high. The space between the cylinders is filled with a liquid whose viscosity is unknown. If a torque of 12.0 Nm is required to rotate the inner cylinder at 100 rpm, determine the viscosity of the fluid. In your answer, draw a well labelled diagram to illustrate this problem and also list any assumptions made. [7]