The slenderness ratio of a 5 m long column hinged at both ends and having a circular cross-section of diameter 16 cm is:
Try it first: pick an option, then read the explanation.
Correct answer: D. 125
Asked in SSC JE 03/03/2017 (Evening)
Detailed Explanation
For a solid circle, I = πd⁴/64 and A = πd²/4, so r = √(I/A) = d/4. Both ends hinged gives le = actual length.
\[ r = \sqrt{\frac{\pi d^4/64}{\pi d^2/4}} = \frac{d}{4} = \frac{16}{4} = 4\ \text{cm} \qquad \lambda = \frac{l_e}{r} = \frac{500}{4} = 125 \]
Why “125” Is Correct
The slenderness ratio is 125.
Why the Other Options Are Wrong
- A. 31.25: 31.25 = 500/16 — dividing by the diameter instead of r = d/4.
- B. 62.5: 62.5 = 500/8 — using r = d/2 (the radius) instead of the radius of gyration.
- C. 100: 100 does not follow from these data.
Key Point
Solid circle: r = d/4. λ = le/r.
Key Concepts for Students
- Radius of gyration is not the geometric radius.
- Hollow circle: r = √(D² + d²)/4.
- Convert lengths to the same unit before dividing.
Practice more: this is question 20 in Columns and Struts MCQs – Part 2. Try the whole set and check every answer instantly.