A steel shaft is to be manufactured either as a solid circular or as circular tube

A steel shaft is to be manufactured either as a solid circular or as circular tube. The shaft is required to transmit a torque of 1200 Nm without exceeding an allowable shear stress of 40 MPa, nor an allowable rate of twist of 0.75º/m. For G = 78GPa, determine: a. The required diameter do of the solid shaft. b. The required outer diameter d2 of the hollow shaft if the thickness t of the shaft is specified as one-tenth of the outer diameter. c. The ratio of diameters (that is, the ratio d2/do and the ratio of the weights of the hollow and solid shafts.