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QJEEM23Ph91e1: JEE Main 2023 Physics - Class 11 JEEM23Ph91e1 Solution: A steel rod has a radius of and a length of . A force of…

A steel rod has a radius of 20 mm20 \mathrm{~mm} and a length of 2.0 m2.0 \mathrm{~m} . A force of 62.8 kN62.8 ~\mathrm{kN} stretches it along its length. Young's modulus of steel is 2.0×1011 N/m22.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} . The longitudinal strain produced in the wire is _____________ ×10−5\times 10^{-5}

Step-by-Step Verified Solution

amp; Strain = stress Y=62.8×103π×(0.02)22×1011amp;=62.8×1033.14×4×10−4×2×1011amp;=2.5×10−4amp;=25×10−5\begin{aligned}& \text { Strain }=\frac{\text { stress }}{Y}=\frac{\frac{62.8 \times 10^3}{\pi \times(0.02)^2}}{2 \times 10^{11}} \\\\& =\frac{62.8 \times 10^3}{3.14 \times 4 \times 10^{-4} \times 2 \times 10^{11}} \\\\& =2.5 \times 10^{-4} \\\\& =25 \times 10^{-5}\end{aligned}

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