A single-plate clutch transmits \(20 \mathrm{~kW}\) at \(1000 \mathrm{rpm}\). The maximum pressure intensity between the plates is \(0.09 \mathrm{MPa}\). The outer diameter of the plate is \(350 \mathrm{~mm}\) and both the sides of the plate are effective. The coefficient of friction is 0.25 . Determine

(a) inner diameter of the plate and

(b) axial force required to engage the clutch.