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?

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:

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