Question

How much force is required to have an increase of 0.2% in the length of a
metallic wire of radius 0.2mm. Given Y = 9 × 1010 N m–2.

Answer 1

change in length, ∆l = 0.2% of length of wire

= 0.2% of l

= 0.2/100 × l

= 0.002l

so strain = ∆l/l = 0.002l/l = 0.002

cross sectional area, A = πr²

= 3.14 × (0.2mm)²

= 3.14 × (2 × 10^-4m)²

= 3.14 × 4 × 10^-8 m²

= 12.56 × 10^-8 m²

now Young's modulus = stress/strain

⇒Y = (F/A)/strain

⇒9 × 10^10 = F/(12.56 × 10^-8 × 0.002)

⇒F = 9 × 10^10 × 12.56 × 10^-8 × 0.002

= 9 × 12.56 × 0.2

= 22.608N [Ans]