Torsion: solid vs. hollow shaft with identical length, weight, and material Two shafts A (solid) and B (hollow) have the same length, weight, and material; both are under pure torsion. State the correct comparative statement about their torsional strength/stiffness.

Given• Same material ⇒ same allowable shear stress (τ_allow) and shear modulus G.• Same length and weight ⇒ for the hollow shaft, material is distributed farther from the center.

ConceptTorque capacity at a given τ scales with the polar section modulus Z_p; torsional stiffness scales with the polar moment of inertia J:T_max = τ_allow · Z_p, θ = T L / (G J)For a given mass, moving material outward (hollowing) increases both J and Z_p, hence higher torque capacity and lower twist.

ResultA hollow shaft of equal weight/length is stronger in torsion and has greater torsional rigidity than a solid shaft.

Final AnswerThe hollow shaft is stronger and stiffer for the same weight