Question

Calculate the force required to produce
an elongation of 0.1 cm in a steel wire
of radius 1 mm and length 2 m. (Young's
modulus of the wire = 20x10^10 N/m²)​

Answer 1

Force required to produce an elongation of 0.1 cm in a steel wire of radius 1 mm and length 2 m is 314 N

Given-

• Initial length of the wire = 2 m
• Radius of wire = 1 mm = 1 × 10⁻³ m
• Elongation of the steel wire = 0.1 cm = 1 × 10⁻³ m

• Young's modulus = 20 × 10¹⁰ N/m²

Let the force required to produce an elongation in the steel wire be F.

We know that

Y = F×L/A×I

F = Y × A × I/ L

F = πr²YI / L

By substituting the values we get

F = 3.14 × (1 × 10⁻³)² × 20 × 10¹⁰ × 1 × 10⁻³ / 2

F = 314 N

Thus the Force required to produce an elongation of 0.1 cm in a steel wire of radius 1 mm and length 2 m is 314 N