In an experiment to determine the Young's modulus, steel wires of five different lengths ( 1 , 2 , 3 , 4 and 5 ) but of same cross-section 2 mm 2 were taken and curves between extension and load

Question

In an experiment to determine the Young's modulus, steel wires of five different lengths ( $1, 2, 3, 4$ and $5$ ) but of same cross-section $(2 {mm}^{2})$ 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 $x \times 10^{11} N m^{- 2}$ , then the value of $x$ is _____ .

TestHub · Accepted Answer

We know that, Young's modulus is Y = F L A ∆ L , where, F is force or load acting on wire, A is cross-section area, L is length and ∆ L is extension in length. Now, from given graph, the slope of the line is = Δ L W L = Δ L L W = 1 Y A ⇒ Y = 1 slope A Thus, Young's modulus of the steel wires is Y = 1 2 × 10 - 6 0 . 25 × 10 - 5 ⇒ Y = 2 × 10 11 N m - 2 . Therefore, x = 2 .

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