If all the dimensions of a prismatic bar are doubled, the maximum stress produced in it under its own weight will:
Try it first: pick an option, then read the explanation.
Correct answer: B. increase to two times
Asked in SSC JE 25/01/2018 (Morning)
Detailed Explanation
A bar hanging from its top carries its own weight. The section at the top supports the whole bar below it.
\[ \sigma_{max} = \frac{\text{weight}}{A} = \frac{\gamma A L}{A} = \gamma L \]
Doubling all dimensions: \(A\) becomes \(4A\) but cancels out; \(L\) becomes \(2L\), so \(\sigma_{max}\) becomes \(2\gamma L\).
Why “increase to two times” Is Correct
The area cancels, so only the length matters. Doubling the length makes the maximum stress two times larger. (Elongation γL²/2E becomes four times.)
Why the Other Options Are Wrong
- A. decrease: The stress grows with length, so it cannot decrease.
- C. increase to three times: Three times has no basis; stress is proportional to L.
- D. None of these: Option (b) is correct.
Key Point
Self-weight stress σ_max = γL; elongation = γL²/2E.
Key Concepts for Students
- Doubling L quadruples the self-weight elongation.
- A bar of uniform strength tapers to keep stress constant.
- Very long cables are limited by their self-weight.
Practice more: this is question 11 in Stress and Strain MCQs – Part 1. Try the whole set and check every answer instantly.