Two shafts of the same length and material are joined in series. If the ratio of their diameters is 2, the ratio of their angles of twist will be:
Try it first: pick an option, then read the explanation.
Correct answer: D. 16
Asked in SSC JE 01/03/2017 (Morning)
Detailed Explanation
Shafts in series transmit the same torque. With equal L and G, θ = 32TL/(πGd⁴) ∝ 1/d⁴.
\[ \frac{\theta_{small}}{\theta_{large}} = \left(\frac{d_{large}}{d_{small}}\right)^4 = 2^4 = 16 \]
Why “16” Is Correct
The thinner shaft twists 16 times as much.
Why the Other Options Are Wrong
- A. 2: θ is not ∝ 1/d.
- B. 4: θ is not ∝ 1/d² (that would be for area).
- C. 8: 8 is the ratio of maximum shear stresses (∝ 1/d³), not of twists.
Key Point
Series: same T, θ ∝ 1/d⁴; τ ∝ 1/d³.
Key Concepts for Students
- Parallel shafts share the same θ.
- Total twist in series = sum of twists.
- Stiffness ∝ d⁴.
Practice more: this is question 29 in Torsion MCQs – Part 2. Try the whole set and check every answer instantly.