A 4 meter long solid circular cylindrical shaft transmits 1600 kW at 500 rpm. The endurance limit of the material is 210 MPa and a factor of safety of 3 is to be used with respect to fatigue failure. Use G = 77.5 GPa. The design diameter ‘D’ of the shaft in metre is

• A. \(3\sqrt {\frac{{69}}{{4375{\pi^2}}}} \)
• B. \(3\sqrt {\frac{{4375}}{{96{\pi^2 }}}} \)
• C. \(3\sqrt {\frac{{69}}{{4735{\pi^2 }}}} \)
• D. \(3\sqrt {\frac{{192}}{{4375{\pi^2}}}} \)