Axial strain calculation: A bar of length L metres extends by l millimetres under a tensile force P. What is the engineering strain produced in the bar?
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Al / L
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B0.1 l / L
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C0.01 l / L
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D0.001 l / L
Answer
Correct Answer: 0.001 l / L
Explanation
Introduction / Context:Strain is the non-dimensional measure of deformation and is defined as change in length divided by original length. Careful unit handling is essential when lengths are given in different units.
Given Data / Assumptions:
- Original length = L metres.
- Extension = l millimetres.
- Small, uniform axial strain (linear elastic range).
Concept / Approach:Engineering strain epsilon = delta_L / L_0. Convert all lengths to consistent units before forming the ratio to ensure a dimensionless quantity.
Step-by-Step Solution:
Convert extension to metres: delta_L = l mm = (l / 1000) m.Original length L_0 = L m.Compute strain: epsilon = (l / 1000) / L = 0.001 * (l / L).Hence epsilon = 0.001 l / L (dimensionless).Verification / Alternative check:Unit check: numerator and denominator both in metres; the ratio is unitless as required for strain.
Why Other Options Are Wrong:
- l / L: ignores unit conversion; would be 1000× too large.
- 0.1 l / L and 0.01 l / L: incorrect conversion factors.
Common Pitfalls:Forgetting to convert millimetres to metres or mixing up engineering strain with percentage strain (%strain = 100 * epsilon).
Final Answer:0.001 l / L