A 0.600-mm diameter wire stretches 0.500% of its length when it is stretched with a tension of 20.0 N.What is the Young's modulus of this wire? A) 5.66 × 10¹⁰ N/m² B) 3.54 × 10⁹ N/m² C) 1.41 × 10¹⁰ N/m² D) 6.43 × 10⁹ N/m² E) 2.78 × 10⁹ N/m²

Question

Quizplus · Accepted Answer

We can use the formula for Young's modulus:
Y = (F/A)/(∆L/L)
where F is the tension, A is the cross-sectional area, ∆L is the change in length, and L is the original length.
First, we need to find the cross-sectional area of the wire. The diameter is given as 0.600 mm, so the radius is 0.300 mm or 0.0003 m. The area is then:
A = πr^2 = π(0.0003 m)^2 = 2.83 × 10^-7 m^2
Next, we can plug in the given values:
Y = (20 N/2.83 × 10^-7 m^2)/(0.005) = 1.41 × 10^11 N/m^2
Therefore, the answer is choice C.

A 0600-Mm Diameter Wire Stretches 0