Analysis of Stress versus Strain Curve with Swapped Axes

To determine the correct statements, let us analyze the given graph step-by-step:

1. Young's Modulus ($Y$)

Young's modulus is defined as the ratio of tensile stress ($\sigma$) to tensile strain ($\varepsilon$): $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\sigma}{\varepsilon}$

In the given graph, strain is plotted along the $y$-axis ($\varepsilon$) and stress is plotted along the $x$-axis ($\sigma$). Therefore, the slope $m$ of the linear proportional region is given by: $m = \frac{y}{x} = \frac{\varepsilon}{\sigma} = \frac{1}{Y} \implies Y = \frac{1}{m}$

From the graph:

• The line for $P$ is steeper than that for $Q$ in the linear region, meaning $m_P > m_Q$.
• Since Young's modulus is inversely proportional to the slope of this graph, we have: $Y_P < Y_Q$ Thus, the Young's modulus of $P$ is less than that of $Q$. Option (D) is incorrect.

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2. Tensile Strength

Tensile strength refers to the maximum stress a material can withstand before fracture (ultimate tensile stress).

• Since stress is represented along the horizontal $x$-axis, the ultimate tensile strength corresponds to the maximum $x$-coordinate reached by the curve.
• From the graph, curve $P$ extends further to the right along the $x$-axis than curve $Q$, which means: $\sigma_{\text{max}, P} > \sigma_{\text{max}, Q}$

Thus, material $P$ has a higher tensile strength than material $Q$. Option (A) is correct.

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3. Ductility and Brittleness

Ductility is measured by the amount of plastic strain (permanent deformation) a material undergoes before breaking. Brittleness implies that a material breaks with very little plastic deformation beyond its elastic limit.

• Strain is represented along the vertical $y$-axis.
• Curve $P$ extends significantly higher along the $y$-axis into the plastic region, indicating a much higher strain at fracture compared to curve $Q$.
• Since $P$ undergoes much larger plastic deformation before fracture, material $P$ is more ductile and less brittle than material $Q$.

Thus, Option (B) is correct and Option (C) is incorrect.

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Final Conclusion

The valid statements are (A) and (B).