Physics, asked by suryaraghav20, 11 months ago

A wire of diameter 3 mm and length 4 m extends by
2.5 mm when a force of 10 N is applied. Find the
Young's modulus of material of wire.​

Answers

Answered by BrainlyConqueror0901
27

\blue{\bold{\underline{\underline{Answer:}}}}

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

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

 \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 = ?}

• According to given question :

  : \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}  }

Answered by BendingReality
21

Answer:

3.4 × 10⁷ N / m² .

Explanation:

Given :

Diameter of wire = 3 mm or 3 / 2 × 10⁻³ m

Length of wire = 4 m

Force = 10 N

Change in length = 2.5 mm or 2.5 × 10⁻³ m

Cross section area = π ( 3 / 2 × 10⁻³ )² m²

We know :

Y = F / A × L / Δ L

Y = 10 / π ( 3 / 2 × 10⁻³ )² × 4 / 2.5 × 10⁻³ N / m²

Y = 3.4 × 10⁷ N / m² .

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