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The stress experienced by a wire of diameter \(\frac{\text{y}}{\pi}\)m loaded by a weight y\(^2\)N is

Physics
JAMB 2024

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\(^{-2}\)
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Correct Answer: Option 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\(^{-2}\)

There is an explanation video available below.


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Explanation Video

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