A lift cage of mass 4000 kg is raised by a hoist drum of mass 750 kg, diameter 1.5 m and radius of gyration 600 mm. The cage is accelerated from rest through a distance of 12 m at the rate of 1.5 m s 2 against a friction torque of 3 kNm. Calculate (a) the final angular velocity of the drum, (b) the angular acceleration of the drum, (c) the work done by the driving motor, (d) the input torque to the drum, (e) the maximum power developed by the driving motor.