Question

Define Young’s Modulus of elasticity. How much force is required to have an increase of 0.4% in the length of a metallic wire having radius of 0.2mm. ( See Lesson 8) Y = 9.1 x 1010 Nm–2​

Answer 1

Explanation:

Young’s Modulus or Elastic Modulus or Tensile Modulus, is the measurement of mechanical properties of linear elastic solids like rods, wires, etc.

The Young's Modulus (or Elastic Modulus) is in essence the stiffness of a material. In other words, it is how easily it is bended or stretched. To be more exact, the physics and numerical values are worked out like this:

$youngs \: modulus = \frac{stress}{strain}$

$stress = \frac{force}{area}$

$strain = \frac{change \: in \: length}{original \: length}$

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Answer 2

We have to define Young's modulus of elasticity and also find force which is required to have an increase of 0.4 % in the length of a metallic wire having radius of 0.2 mm.

solution : Young's modulus of elasticity : Young's modulus is a measure of ability of a metal to resist changes in length of metal under the lengthwise tension or compression.

mathematically,

Young's modulus is the ratio of stress to strain.

here, ∆l = 0.4% of l

⇒∆l = 4 × 10¯³l

r = 0.2 mm

so, cross sectional area, A = πr²

= 3.14 × (2 × 10¯⁴ m)²

= 3.14 × 4 × 10^-8 m²

= 1.256 × 10^-7 m²

γ = 9.1 × 10¹⁰ N/m²

using formula, γ = Fl/A∆l

⇒9.1 × 10¹⁰ = F × l/(1.256 × 10^-7 × 4 × 10¯³l)

⇒9.1 × 10¹⁰ × 1.256 × 4 × 10¯¹⁰ = F

⇒F = 45.7184 N ≈ 45.72 N

Therefore The force needed to increase the length of metallic wire is 45.72 N (approx.)