Pick the incorrect statement. The torsional resistance of a shaft is directly proportional to:
Try it first: pick an option, then read the explanation.
Correct answer: D. moment of inertia of the shaft section
Asked in SSC JE 22/01/2018 (Morning); SSC JE 27/01/2018 (Morning)
Detailed Explanation
Torsional resistance T = GJθ/L from the torsion equation.
\[ T = \frac{G J \theta}{L} \]
Why “moment of inertia of the shaft section” Is Correct
T is proportional to G, θ and 1/L — all true. It depends on the polar moment of inertia J, so saying "moment of inertia" (i.e. I about a diameter) is the incorrect statement in the book's key.
Why the Other Options Are Wrong
- A. modulus of rigidity: True: T ∝ G.
- B. angle of twist: True: T ∝ θ.
- C. reciprocal of the length of the shaft: True: T ∝ 1/L.
Key Point
T = GJθ/L — polar moment of inertia J, not the planar I.
Key Concepts for Students
- For a circle J = 2I, so the two are proportional, which is why the wording matters.
- Torsional stiffness GJ/L.
- Hollow shafts give large J.
Practice more: this is question 19 in Torsion MCQs – Part 2. Try the whole set and check every answer instantly.