A tapered bar AB of solid circular cross section is twisted by torques T (see figure). The

Question:

A tapered bar AB of solid circular cross section is twisted by torques T (see figure). The diameter of the bar varies linearly from dA at the left-hand end to dB at the right-hand end.
For what ratio dB/dA will the angle of twist of the tapered bar be one-half the angle of twist of a prismatic bar of diameter dA? (The prismatic bar is made of the same material, has the same length, and is subjected to the same torque as the tapered bar.) Hint: Use the results of Example 3-5.