A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 p ms–2, what will be the tensile stress that would be developed in the wire ?

Properties of Matter PYQ — JEE Main 2019 · 8 Apr · Shift 1 · Q59 with Solution

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Correct answer: A

Given data
- Radius of wire: $r = 2.0\,\text{mm} = 2.0 \times 10^{-3}\,\text{m}$
- Load: $m = 4\,\text{kg}$
- Acceleration due to gravity: $g = 3.1\pi\,\text{m s}^{-2}$
Formula for tensile stress Tensile stress is
$\text{Stress} = \frac{\text{Force}}{\text{Area}}$
Here, force due to load is
$F = mg = 4 \times 3.1\pi = 12.4\pi\,\text{N}$
Cross-sectional area of the wire
$A = \pi r^2 = \pi (2.0 \times 10^{-3})^2$ $A = \pi \times 4 \times 10^{-6} = 4\pi \times 10^{-6}\,\text{m}^2$
Compute stress
$\text{Stress} = \frac{12.4\pi}{4\pi \times 10^{-6}}$ $\text{Stress} = \frac{12.4}{4} \times 10^6$ $\text{Stress} = 3.1 \times 10^6\,\text{N m}^{-2}$
Match with options This corresponds to:
$\boxed{3.1 \times 10^6\,\text{N m}^{-2}}$
So the correct option is A.
Comparison with stored answer Stored correct answer: A

My derived answer also gives A, so they agree.