Discussion
When the same load is applied to an aluminium bar, it is found to give same elastic strain as the steel. Calculate the cross-sectional area of the aluminium bar.
Answer: D
The aluminium bar needs 22.86 cm2.
The elastic strain under axial load is \(\varepsilon = F/(AE)\). Equal strain under the same load means equal axial stiffness per unit length, AE:
\[ \begin{aligned} A_{Al}E_{Al} &= A_{s}E_{s} \\ A_{Al} &= 8 \times \frac{200}{70} = 22.86\ \text{cm}^{2} \end{aligned} \]
Aluminium is less stiff than steel, so it needs a larger area, which rules out 11.43 cm2 (which halves the answer) and points to the largest option. Poisson's ratio and the length play no part here.
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