As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of

Question

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45 °$ with the load axis. The length of wire is $62.8 cm$ and its diameter is $4 mm$ . The Young's modulus is found to be $x \times 10^{4} N m^{- 2}$

The value of $x$ is _______.

TestHub · Accepted Answer

Given here, L = 62 . 8 cm and d = 4 mm . From the given graph, we can see that extension in wire is linearly dependent on force applied. Slope of the curve is tan 45 ° = 1 . So, F = Δ L Young's modulus is given by Y = F L A Δ L , where, A is area of wire. ⇒ Y = L A ⇒ Y = 62 . 8 × 10 - 2 π 2 × 10 - 3 2 ⇒ Y = 5 × 10 4 N m - 2

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