Identify the correct statement related to a circular shaft subjected to pure torsion.
Try it first: pick an option, then read the explanation.
Correct answer: D. The torque required to produce a twist of one radian per unit length of a shaft is termed torsional rigidity.
Asked in SSC JE 06/11/2024 (9 am–11 am)
Detailed Explanation
Test each statement against the torsion equation T/J = τ/R = Gθ/L.
\[ T = GJ\,\frac{\theta}{L} \quad\Rightarrow\quad \frac{\theta}{L} = 1 \Rightarrow T = GJ \]
Why “The torque required to produce a twist of one radian per unit length of a shaft is termed torsional rigidity.” Is Correct
GJ is the torque per unit twist per unit length — the definition of torsional rigidity. Statement (d) is correct.
Why the Other Options Are Wrong
- A. At the outer surface of the shaft the shear stress is zero.: Shear stress is maximum at the outer surface and zero at the centre.
- B. If a moment is applied in a vertical plane containing the longitudinal axis of a beam, it will subject the member to torque causing torsion.: A moment in a plane containing the axis causes bending; torque acts in a plane perpendicular to the axis.
- C. The twist along the shaft is not uniform.: In pure torsion of a uniform shaft the twist per unit length is constant, so the twist varies uniformly along it.
Key Point
Torsional rigidity GJ = torque per unit angle of twist per unit length.
Key Concepts for Students
- Flexural rigidity EI is the bending counterpart.
- Torsional stiffness = GJ/L (torque per radian for the whole length).
- τ is maximum at r = R.
Practice more: this is question 2 in Torsion MCQs – Part 1. Try the whole set and check every answer instantly.