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Q8.2: NCERT Physics - Part 2 MECHANICAL PROPERTIES OF SOLIDS 8.2 Solution: Figure 8.9 shows the strain-stress curve for a given material.…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often compute $Y$ by simply dividing the stress and strain values at a single point on the graph, forgetting that Young's modulus is the *slope* of the initial linear (elastic) region, not a point‑ratio; the correct method is $Y=\Delta\sigma/\Delta\varepsilon$ using two points on the straight‑line portion. Misreading the yield strength as the maximum stress (ultimate tensile strength) is another common slip—yield strength is the stress at which plastic deformation begins, usually identified by the 0.2% offset line, not the peak of the curve.

Figure 8.9 shows the strain-stress curve for a given material. What are (a) Young's modulus and (b) approximate yield strength for this material?

Step-by-Step Verified Solution

**Answer:** (a) Y=7.5×1010 N/m2Y = 7.5 \times 10^{10} \text{ N/m}^2 (b) Yield strength ≈3×108 N/m2\approx 3 \times 10^8 \text{ N/m}^2 **Step-by-Step Explanation:** (a) From the graph, at stress = 150×106150 \times 10^6 N/m_, strain = 0.002.
Y=StressStrain=150×1060.002=7.5×1010 N/m2Y = \frac{\text{Stress}}{\text{Strain}} = \frac{150 \times 10^6}{0.002} = 7.5 \times 10^{10} \text{ N/m}^2
(b) The yield strength is the maximum stress the material can sustain without crossing the elastic limit. From the graph, the approximate yield strength is 300×106300 \times 10^6 N/m_ = 3×1083 \times 10^8 N/m_ [citation:1][citation:11].

All Questions in this Chapter

Q8.1 Q8.2 Q8.3 Q8.4 Q8.5 Q8.6 Q8.7 Q8.8 Q8.9 Q8.10 Q8.11 Q8.12 Q8.13 Q8.14 Q8.15 Q8.16

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