Generalize Prob. 3–62 for a solid shaft of diameter d replaced with a hollow shaft of the same material with an outside diameter d, and an inside diameter that is a fraction of the outside diameter, x × d, where x is any fraction between zero and one. Obtain expressions for percentage reduction in torque transmission and percentage reduction in weight in terms of only x. The length and diameter of the shaft, and the material, are not needed for this comparison. Plot both results on the same axis for the range 0 < x < 1. From the plot, what is the approximate value of x to obtain the greatest difference between the percent decrease in weight and the percent decrease in torque?