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  • A metallic wire of length 2.5 meters and diameter 0.8 mm is subjected to a tensile force of 800 N, causing it to elongate by 2.2 mm. The density of the material of the wire is 7.8 g/cm3

A metallic wire of length 2.5 meters and diameter 0.8 mm is subjected to a tensile force of 800 N, causing it to elongate by 2.2 mm. The density of the material of the wire is 7.8 g/cm3 . Calculate the Young’s modulus of elasticity of the material of the wire.

Option: 1

9.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^2


Option: 2

1.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2


Option: 3

2.4 \times 10^{11} \mathrm{~N} / \mathrm{m}^2


Option: 4

3.6 \times 10^{11} \mathrm{~N} / \mathrm{m}^2


Answers (1)

best_answer

Young’s modulus (Y ) is a measure of the stiffness of a material. It’s defined as the ratio of stress (σ) to strain (?) and is given by the formula:

Y=\frac{\text { Stress }}{\text { Strain }}

Where: Stress (σ) = Force / Area Strain (?) = Change in length / Original length Given data:

Original length (L) = 2.5 m Diameter (d) = 0.8 mm Tensile force (F) = 800 N Elongation (?L) = 2.2 mm Density (ρ) = 7.8 g/cm3 First, let’s calculate the cross-sectional area (A) of the wire using its diameter:

A=\frac{\pi d^2}{4}

Now, convert diameter to meters and calculate area:

A=\frac{\pi \times\left(0.8 \times 10^{-3}\right)^2}{4} \mathrm{~m}^2

Next, calculate the strain (?) using the elongation and original length:

\epsilon=\frac{\Delta L}{L}

Convert elongation to meters and calculate strain:

\epsilon=\frac{2.2 \times 10^{-3}}{2.5} \mathrm{~m}

Now, calculate stress (σ) using the formula σ = F/A :

\sigma=\frac{F}{A}

Substitute the given values:

\sigma=\frac{800}{\frac{\pi \times\left(0.8 \times 10^{-3}\right)^2}{4}} \mathrm{~N} / \mathrm{m}^2

Finally, calculate Young’s modulus (Y ) using the formula Y = σ/? :

Substitute the calculated values for stress and strain:

Y=\frac{\frac{800}{\frac{\pi \times\left(0.8 \times 10^{-3}\right)^2}{4}}}{\frac{2.2 \times 10^{-3}}{2.5}} \mathrm{~N} / \mathrm{m}^2

Solve for Y , and you’ll find that the value is approximately 1.2×1011 N/m2 , which corresponds to option B.

 

Posted by

vishal kumar

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