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A wire of diameter 0.20 mm stretches by 0.20% when a 6.28-N force is applied. What is the elastic modulus (aka Young's modulus) of the wire?

a. 2.5 x 10¹⁰ N/m²
b. 2.5 x 10¹² N/m²
c. 1.0 x10¹² N/m²
d. 1.0 x 10¹¹ N/m²

1 Answer

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The elastic modulus (aka Young's modulus) of the wire is 1.0 x 10¹¹ N/m² (Option D).

How to Calculate the elastic modulus?

The formula for elastic modulus or Young's modulus of elasticity is given as:

E = stress / strain

The stress applied to the wire is calculated as follows:

stress = Force / Area

Area = 3.14 x (0.0001 m)²

Area = 3.14 x 10⁻⁸ m²

The stress is calculated as:

Stress = (6.28 N ) / (3.14 x 10⁻⁸ m²)

Stress = 2 x 10⁸ N/m²

The strain of the wire is calculated as follows:

strain = 0.2 % / 100

strain = 0.002

The Young's modulus is calculated as:

E = stress / strain

E = 2 x 10⁸ N/m² / 0.002

E = 1 x 10¹¹ N/m²

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