A torsion member is made from two concentric thin tubes welded at the ends to rigid discs so that both twist as a unit. The radius of the outer tube is 2r and of the inner tube r. If the shear stress in the outer tube is T, the shear stress in the inner tube is:
Try it first: pick an option, then read the explanation.
Correct answer: D. 0.5T
Asked in SSC JE 01/03/2017 (Evening)
Detailed Explanation
The rigid end discs force both tubes to twist through the same angle over the same length, just like layers of a single shaft.
\[ \frac{\tau}{\rho} = \frac{G\theta}{L} = \text{const} \;\Rightarrow\; \frac{\tau_{in}}{\tau_{out}} = \frac{r}{2r} \;\Rightarrow\; \tau_{in} = 0.5\,T \]
Why “0.5T” Is Correct
The inner tube's shear stress is 0.5T (assuming the same material).
Why the Other Options Are Wrong
- A. T: Equal stress would need equal radii.
- B. 0.25T: 0.25T would follow from τ ∝ ρ², but it is linear.
- C. 0.75T: 0.75T has no basis.
Key Point
Same twist: shear stress ∝ radius (τ = Gρθ/L).
Key Concepts for Students
- Same logic as stress across a solid shaft.
- Torque shares are in proportion to each tube's GJ.
- Different materials would scale by G.
Practice more: this is question 24 in Torsion MCQs – Part 2. Try the whole set and check every answer instantly.