Torsional rigidity of a shaft: it is the torque required to produce a twist of one radian per unit length of the shaft. State whether this definition is correct.

Introduction / Context:Torsional rigidity quantifies a shaft's resistance to twisting under applied torque. It is fundamental for drive shafts, transmission lines, and rotary machine elements where angular deflection control is important.

Given Data / Assumptions:

• Uniform, prismatic shaft of length L.
• Linear elastic behavior and Saint-Venant torsion assumption.
• Polar moment of inertia J depends on cross-section.

Concept / Approach:Torsion relation: theta = T L / (G J), where theta is the twist in radians, T is torque, G is shear modulus, and J is polar moment. Rearranging defines torsional rigidity G J as the torque per unit twist per unit length.

Step-by-Step Solution:

Verification / Alternative check:Dimensional check: G (stress) * J (length^4) gives torque per radian per unit length.

Why Other Options Are Wrong:Depends on cross-section (solid or hollow) through J; definition remains valid for both.Using degrees would require conversion; radians are standard.

Common Pitfalls:Confusing torsional rigidity (GJ) with bending rigidity (EI); forgetting that J differs significantly between solid and hollow shafts for the same area.

Final Answer:

True