Properties of matterMedium
Question
The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are $8 \times 10^{8}\text{ }N{\text{ }m}^{- 2}$ and $2 \times 10^{11}\text{ }N{\text{ }m}^{- 2}$, is:
Options
A.40 mm
B.8 mm
C.4 mm
D.0.4 mm
Solution
Sol. [Key Concept: Elongation of a wire within the elastic limit (Hooke's law)] In the case for maximum elongation,
Stress $=$ Elastic limit
$$\begin{matrix} \delta_{\max} = \frac{\sigma_{\text{elastic}\text{~}} \times L}{\text{~}\text{Young's modulus}\text{~}} = \frac{8 \times 10^{8} \times 1}{2 \times 10^{11}} & \ = 4 \times 10^{- 3} \\ & \ = 4\text{ }mm \end{matrix}$$
i.e. maximum elongation is 4 mm
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