Question

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) 6.43 × 109 N/m2
B) 1.41 × 1010 N/m2
C) 5.66 × 1010 N/m2
D) 2.78 × 109 N/m2
E) 3.54 × 109 N/m2

Answer 1

(B) 1.41 x 10^{10} N/m^{2}

Step-by-step explanation:

diameter of wire (d) = 0.6 mm = 0.0006 m

radius of wire (r) = 0.0006/2 = 0.0003 m

tension (force F) = 20 N

percentage strain = 0.5 %

what is the Young's modulus?

Young's modulus =
`(stress)/(strain)`

where

• stress = force/area

stress =
`(force)/(πr^(2))`

stress =
`(20)/(πx0.0003^(2))`

stress =70735530.3 N/m^{2}

• strain = percentage strain ÷ 100

strain = 0.5 ÷ 100 = 0.005

therefore Young's modulus =
`(stress)/(strain)` =
`(70735530.3)/(0.005)` = 1.41 x 10^{10} N/m^{2}