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JEE Main 2022 (27 Jul, Shift 2) · Wire Combinations & Special Cases

Wire Combinations & Special Cases question from JEE Main 2022 (27 Jul, Shift 2)

Q16JEE Main 2022 · 27 JUL · SHIFT 2Medium

Wire Combinations & Special Cases

In an experiment to determine the Young's modulus, steel wires of five different lengths (1,2,3,4(1, 2, 3, 4, and 5 m)5\text{ m}) but of same cross section (2 mm2)\left(2\text{ mm}^2\right) 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×1011 Nm−2x \times 10^{11}\text{ Nm}^{-2}, then the value of xx is __________.

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 2

  1. ΔlF=LAY\frac{\Delta l}{F} = \frac{L}{AY}, so the graph slope is 1AY\frac{1}{AY}.
  2. From the graph, slope =0.25×10−51=2.5×10−6= \frac{0.25 \times 10^{-5}}{1} = 2.5 \times 10^{-6} per m
  3. Y=1A×2.5×10−6=12×10−6×2.5×10−6=2×1011 N m−2Y = \frac{1}{A \times 2.5 \times 10^{-6}} = \frac{1}{2 \times 10^{-6} \times 2.5 \times 10^{-6}} = 2 \times 10^{11}\text{ N m}^{-2}
  4. So x=2x = 2.
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