A cone clutch of semi-cone angle \(15^{\circ}\) is used to transmit \(30 \mathrm{~kW}\) at \(800 \mathrm{rpm}\). The mean frictional surface radius is \(150 \mathrm{~mm}\) and normal intensity of pressure of the mean radius is not to exceed \(0.15 \mathrm{MPa}\). The coefficient of friction is 0.2 . Assuming uniform wear, determine:

(a) Width of contact surface, and

(b) Axial force required to engage the clutch