In a shaft, the shear stress is NOT directly proportional to the:
Try it first: pick an option, then read the explanation.
Correct answer: C. length of the shaft
Asked in SSC JE 25/01/2018 (Evening)
Detailed Explanation
Rearrange the torsion equation for τ.
\[ \frac{\tau}{R} = \frac{G\theta}{L} \;\Rightarrow\; \tau = \frac{G R\theta}{L} \]
Why “length of the shaft” Is Correct
τ is directly proportional to R, θ and G, but inversely proportional to the length L.
Why the Other Options Are Wrong
- A. radius of the shaft: τ ∝ R — directly proportional.
- B. angle of twist: τ ∝ θ — directly proportional.
- D. modulus of rigidity: τ ∝ G — directly proportional.
Key Point
τ = GRθ/L: ∝ G, R, θ; ∝ 1/L.
Key Concepts for Students
- For a given torque, τ = TR/J is independent of L.
- Longer shaft → more twist for the same stress.
- Shear strain γ = Rθ/L.
Practice more: this is question 14 in Torsion MCQs – Part 1. Try the whole set and check every answer instantly.