Bar ‘A’ has diameter d and length L. Bar ‘B’ has diameter 2d and length 2L. The ratio of extension of bar A to extension of bar B is
- A4
- B2Correct
- C0.5
- D0.25
Solution
Concept
Extension under the same axial load
Formula
δ = P L / (A E)
Step-by-step solution
1. Same load and material: δ ∝ L / A ∝ L / d². 2. δA : δB = (L/d²) : (2L/(2d)²) = (L/d²) : (L/2d²). 3. Ratio = 2.
Explanation
For the same axial force the extension is proportional to length and inversely proportional to the area (d²).
Why the other options are wrong
4 would result from ignoring the doubling of length; 0.5 and 0.25 are the inverse ratios.
Shortcut
δ ∝ L/d².
Common mistake
Forgetting that area varies as d².
Correct answer: B) 2