Question

A 100-N weight is attached to a free end of a metallic wire that hangs from the ceiling. When a second 100-N weight is added to the wire, it stretches 3.0 mm. The diameter and the length of the wire are 1.0 mm and 2.0 m, respectively. What is Young’s modulus of the metal used to manufacture the wire?

a) 1.38 × 10^11 N/m²
b) 1.84 × 10^11 N/m²
c) 2.19 × 10^11 N/m²
d) 2.55 × 10^11 N/m²

Answer 1

Young's modulus of the metal used to manufacture the wire is 1.38 × 10^11 N/m².

Step-by-step explanation:

To find Young's modulus of the metal used to manufacture the wire, we can use the formula:

Young's modulus (Y) = (stress / strain) * (length / original length)

First, let's calculate the stress:

Stress = force / area

The force applied is the weight, which is 100 N. The area can be calculated using the formula for the area of a circle:

Area = π * (diameter / 2)^2

Plugging in the values, we get:

Area = π * (1.0 mm / 2)^2 = 0.785 mm^2

Now, let's calculate the strain:

Strain = change in length / original length

The change in length is 3.0 mm and the original length is 2.0 m, which is equal to 2000 mm. So:

Strain = 3.0 mm / 2000 mm = 0.0015

Finally, we can plug in the values into the formula for Young's modulus:

Young's modulus (Y) = (100 N / 0.785 mm^2) * (2000 mm / 3.0 mm) = 132.07 x 10^6 N/m²

Therefore, the correct option is a) 1.38 × 10^11 N/m².