Question

A polymer wire of fifty meter length is tied vertically with a load of two thousand kilogram, calculate the necessary radius of the wire. The maximum elongation and stress are three centimeter and five thousand pascal respectively. Young’s modulus is fifty kilopascal.

Answer 1

There is something wrong with the question. The value of Young's modulus is wrong. I'll explain why

Given data,

Length of wire, L = 50 m

Load attached, m = 2000 Kg

Maximum elongation, l = 3 cm = 0.03 m

Stress = 5000 Pa

Young's modulus value is not required to calculate the radius of the wire

Since, stress = Force/Area = m x g/ π x r^2

⇒ 5000 Pa = (2000 Kg x 9.81 m/s^2) / (π x r^2)

⇒ r^2 = 2000 Kg x 9.81 m.s^-2 / (π x 5000 Kg.m^-1.s^-2)

(Since Pa = Kg.m^-1.s^-2)

⇒ r^2 = 1.249 m^2

⇒ r = 1.1176 m

Why given Young's modulus is wrong?

Since, Strain = Change in length / Original Length

⇒ Strain = 0.03m/50m

⇒ Strain = 0.0006

Young's Modulus, Y = Stress / Strain

⇒ Y = 5000 Pa / 0.0006

⇒ Y = 8,333,333.33 Pa

⇒ Y = 8.33 MPa