Question

A metal wire breaks when a tensile force of 100 N is applied. If the diameter of the wire is 2 mm, the breaking stress of the wire is

• A. $\dfrac{10^8}{\pi}$ Pa
• B. $\dfrac{2 \times 10^8}{\pi}$ Pa
• C. $100 \pi$ Pa
• D. $10^7$ Pa

Hint:

Always convert mm to meters before calculating area when computing stress or pressure.

Answer 1

The Correct Option is A

Stress = $\dfrac{\text{Force}}{\text{Area}}$ = $\dfrac{F}{A}$
Given: $F = 100$ N, diameter = 2 mm = $2 \times 10^{-3}$ m ⇒ radius = $r = 10^{-3}$ m
Area $A = \pi r^2 = \pi (10^{-3})^2 = \pi \times 10^{-6}$ m$^2$
So, Stress = $\dfrac{100}{\pi \times 10^{-6}} = \dfrac{10^8}{\pi}$ Pa