JEE MAIN - Physics (2022 - 27th July Evening Shift - No. 16)
In an experiment to determine the Young's modulus, steel wires of five different lengths $$(1,2,3,4$$, and $$5 \mathrm{~m})$$ but of same cross section $$\left(2 \mathrm{~mm}^{2}\right)$$ 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 $$x \times 10^{11} \,\mathrm{Nm}^{-2}$$, then the value of $$x$$ is __________.
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Answer
2
Explanation
$$Y = {{F \times l} \over {A \times \Delta l}}$$
$$ = {1 \over A} \times {{Wire\,length} \over {{{Extension} \over {load}}}}$$
$$Y = {1 \over A} \times \left( {{1 \over {0.25 \times {{10}^{ - 5}}}}} \right)$$
$$Y = {10^{11}} \times 2$$
$$ \Rightarrow x = 2$$
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