Question

Answer:​​

\green{\therefore{\text{young 's \: modulus}}= 3.4 \times {10}^{7}N/m^{2}}∴young ’s  modulus=3.4×107N/m2

\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}Step−by−stepexplanation:​​

\begin{lgathered}\green{ \underline\bold{Given : }} \\ : \implies \text{Diameter \: of \: wire (d)= 3mm = 3} \times {10}^{ - 4} m \\ \\ : \implies \text{Length \: of \: wire (l)= 4m} \\ \\ : \implies \text{Change \: in \: length}( \Delta \: l) = 2.5mm = 2.5 \times {10}^{ - 4} m \\ \\ : \implies \text{force = 10 N} \\ \\ \red{ \underline\bold{To \: Find : }} \\ : \implies \text{young 's \: modulus = ?}\end{lgathered}Given:​:⟹Diameter  of  wire (d)= 3mm = 3×10−4m:⟹Length  of  wire (l)= 4m:⟹Change  in  length(Δl)=2.5mm=2.5×10−4m:⟹force = 10 NToFind:​:⟹young ’s  modulus = ?​

• According to given question :

\begin{lgathered}: \implies \text{young 's \: modulus} = \frac{ \text{strees}}{ \text{strain}} \\ \\ : \implies\text{young 's \: modulus} = \frac{ \frac{force}{area} }{ \frac{change \: in \: length}{original \: length} } \\ \\ : \implies\text{young 's \: modulus} = \frac{f \times l}{A \times \Delta} \\ \\ : \implies\text{young 's \: modulus} = \frac{10 \times 4}{\pi {r}^{2} \times 2.5 \times {10}^{ - 4} } \\ \\ : \implies\text{young 's \: modulus} = \frac{40}{3.14 \times 1.5 \times {10}^{ - 4} \times 2.5 \times {10}^{ - 4} } \\ \\ : \implies\text{young 's \: modulus} = \frac{40 \times {10}^{2} \times 10 \times 10 \times {10}^{8} }{314 \times 15 \times 25 } \\ \\ : \implies\text{young 's \: modulus} = \frac{4 \times {10}^{12} }{117750} \\ \\ : \implies\text{young 's \: modulus} = 0.0000339702 \times {10}^{12} \\ \\ \green{ : \implies\text{young 's \: modulus} = 3.4 \times {10}^{7}N/m^{2} }\end{lgathered}:⟹young ’s  modulus=strainstrees​:⟹young ’s  modulus=originallengthchangeinlength​areaforce​​:⟹young ’s  modulus=A×Δf×l​:⟹young ’s  modulus=πr2×2.5×10−410×4​:⟹young ’s  modulus=3.14×1.5×10−4×2.5×10−440​:⟹young ’s  modulus=314×15×2540×102×10×10×108​:⟹young ’s  modulus=1177504×1012​:⟹young ’s  modulus=0.0000339702×1012:⟹young ’s  modulus=3.4×107N/m2​

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Answer 1

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Answer 2

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