The stress experienced by a wire of diameter \(\frac{\text{y}}{\pi}\)m loaded by a weight y\(^2\)N is
A
\(\pi\)Nm\(^{-2}\)
B
2\(\pi\)Nm\(^{-2}\)
C
4\(\pi\)Nm\(^{-2}\)
D
8\(\pi\)Nm\(^{-2}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Stress = \(\frac{force}{area}\)
Force = weight = y\(^2\), Area = \(\pi\)r\(^2\), Diameter = \(\frac{\text{y}}{\pi}\)m ⇒ r = \(\frac{\text{y}}{2\pi}\)m
Stress = \(\frac{y^2}{\pi \times\frac{y^2}{(2\pi)^2}}\)
= \(\frac{y^2}{\pi y^2} \times 4(\pi)^2\) = 4\(\pi\)Nm\(^{-2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70351)