The stress experienced by a wire of diameter \(\frac{\text{y}}{\pi}\)m loaded by a weight y\(^2\)N is
- \(\pi\)Nm\(^{-2}\)
- 2\(\pi\)Nm\(^{-2}\)
-
4\(\pi\)Nm\(^{-2}\)
- 8\(\pi\)Nm\(^{-2}\)
The correct answer is: C
Explanation
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\(^{-2}\)
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