Design a solid steel shaft supported in bearings which carries the rotor of a turbine at the middle. The rotor has a mass of \(250 \mathrm{~kg}\) and delivers a power of \(150 \mathrm{~kW}\) at \(3000 \mathrm{rpm}\). In order to keep the stress due to the unbalance in the rotor small, the critical speed of the shaft is to be made one-fifth of the operating speed of the rotor. The length of the shaft is to be made equal to at least 30 times its diameter.