JAMB - Physics (2024 - No. 1)

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\(^{-2}\)

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\(^{-2}\)