Properties of Matter 1 Question 4
4. A steel wire having a radius of $2.0 mm$, carrying a load of $4 kg$, is hanging from a ceiling. Given that $g=3.1 \pi ms^{-2}$, what will be the tensile stress that would be developed in the wire?
(a) $6.2 \times 10^{6} Nm^{-2}$
(b) $5.2 \times 10^{6} Nm^{-2}$
(c) $3.1 \times 10^{6} Nm^{-2}$
(d) $4.8 \times 10^{6} Nm^{-2}$
(2019 Main, 8 April I)
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Answer:
Correct Answer: 4. (c)
Solution:
- Given, radius of wire, $r=2 mm=2 \times 10^{-3} m$ Weight of load, $m=4 kg, g=3.1 \pi ms^{-2}$
$\therefore$ Tensile stress $=\frac{\text { Force }(F)}{\text { Area }(A)}=\frac{m g}{\pi r^{2}}$
$$ =\frac{4 \times 3.1 \times \pi}{\pi \times\left(2 \times 10^{-3}\right)^{2}}=3.1 \times 10^{6} Nm^{-2} $$
