A 4 meter long solid circular cylindrical shaft transmits 1600 kW at 500 rpm. The endurancelimit 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

$$\sqrt[3]{\frac{69}{4375 \pi^2}}$$

B

$$\sqrt[3]{\frac{4375}{96 \pi^2}}$$

C

$$\sqrt[3]{\frac{69}{4735 \pi^2}}$$

D

$$\sqrt[3]{\frac{96}{4375 \pi^2}}$$