A solid bar 50 mm in diameter and 2000 mm long consists of a steel and aluminum part joined together. When axial force P is applied to the system, a strain gauge attached to the aluminum indicates an axial strain of 800 µm/m. What is the corresponding axial strain on the Steel? Assume $$E_{st}$$​ = 200 GPa and $$E_{Al}$$​ = 70 Gpa.

Correct option is C

​$$\textbf{Given:} \\\text{Strain in aluminum:} \\\varepsilon_{Al} = 800\, \mu\text{m/m} = 800 \times 10^{-6} \\\\E_{Al} = 70\, \text{GPa} \\E_{st} = 200\, \text{GPa}$$

$$\text{Under equal axial force per unit area (same load per area ratio, such as for same diameter), the stress is the same, so:} \\\frac{\sigma_{Al}}{E_{Al}} = \varepsilon_{Al}, \quad \frac{\sigma_{st}}{E_{st}} = \varepsilon_{st} \\\\\text{If the force in both materials is same (force shared equally due to geometry), and both bars experience same axial deformation } (\delta), \text{ then:} \\\delta = \varepsilon_{Al} \cdot L_{Al} = \varepsilon_{st} \cdot L_{st} \\\\\text{But lengths aren't given separately, so assuming equal length or same elongation under same load, the forces in each are proportional to stiffness.} \\\\\text{So,} \quad \frac{\varepsilon_{st}}{\varepsilon_{Al}} = \frac{E_{Al}}{E_{st}} = \frac{70}{200} = 0.35 \\\\\textbf{Strain in Steel:} \\\varepsilon_{st} = 0.35 \times \varepsilon_{Al} = 0.35 \times 800 \times 10^{-6} = 280 \times 10^{-6}$$​​​