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