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In an experiment to determine the Young's modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm²) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}$ Nm^–2, then the value of $x$ is ________ .

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answer is 2.

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Detailed Solution

$\begin{array}{l} Slope = \frac{Δl / w}{L} = \frac{Δl / L}{w} = \frac{1}{YA} \\ \Rightarrow Y = \frac{1}{(slope) A} \\ Y = \frac{1}{2 \times 10^{- 6} (0 .25 \times 10^{- 5})} \\ Y = 2 \times 10^{11} N / m^{2} \end{array}$

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