The ratio of Young's moduli of two materials, E₁/E₂, is 2.5. Bars of the two materials have the same length and area and carry the same force P. The ratio of their elongations δl₁/δl₂ is:
Try it first: pick an option, then read the explanation.
Correct answer: D. 0.4
Asked in SSC JE 04/12/2023 (9 am–11 am)
Detailed Explanation
The elongation of a bar under axial load is δl = PL/(AE). If load, length and area are the same, only E differs, and elongation is inversely proportional to E.
\[ \frac{\delta l_1}{\delta l_2} = \frac{PL/(AE_1)}{PL/(AE_2)} = \frac{E_2}{E_1} = \frac{1}{2.5} = 0.4 \]
Why “0.4” Is Correct
The stiffer bar (higher E) stretches less. Bar 1 is 2.5 times stiffer, so it stretches 1/2.5 = 0.4 times as much — option (d).
Why the Other Options Are Wrong
- A. 2.5: 2.5 is E₁/E₂ — the inverse of the required ratio.
- B. 2: 2 does not come from the data.
- C. 1: Elongations would be equal only if E were equal.
Key Point
δl = PL/AE ⇒ for equal P, L, A: δl₁/δl₂ = E₂/E₁.
Key Concepts for Students
- Axial stiffness of a bar = AE/L.
- Stress is the same in both bars (same P and A); only strain differs.
- Composite bars in parallel share load in proportion to AE.
Practice more: this is question 7 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.