Question

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus, respectively, are 8 × 10⁸ Nm⁻² and 2 × 10¹¹ Nm⁻², is ______.

विकल्प

• 40 mm

• 8 mm

• 4 mm

• 0.4 mm

Answer 1

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus, respectively, are 8 × 10⁸ Nm⁻² and 2 × 10¹¹ Nm⁻², is 4 mm.

Explanation:

Given: Length (l) = 1 m

Elastic limit (σ) = 8 × 10⁸ Nm⁻²

Young’s modulus (Y) = 2 × 10¹¹ Nm⁻²

Young’s modulus (Y) = `"Stress"/"Strain"`

The strain is defined as the ratio of the change in length (ΔL) to the original length (L):

Strain = `(Delta L)/L`

By substituting the expression for strain into the Young's modulus formula, we can solve for the maximum elongation (ΔL):

ΔL = `("Stress" xx L)/Y`

= `(8 xx 10^8 xx 1)/(2 xx 10^11)`

= 4 × 10⁻³ m

= 0.004 m

= 4 mm

∴ The maximum elongation of the steel wire is 4 mm.