A steel wire having a radius of 2.0 , mm, car | vedclass

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(D) The tensile stress $(\sigma)$ in the wire is defined as the ratio of the tensile force $(F)$ to the cross-sectional area $(A)$.Given:Radius $(r)$

Vedclass · Accepted Answer

$3.1 	imes 10^6 \, N/m^2$

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(D) The tensile stress $(\sigma)$ in the wire is defined as the ratio of the tensile force $(F)$ to the cross-sectional area $(A)$.Given:Radius $(r)$ = $2.0 \, mm = 2.0 	imes 10^{-3} \, m$Load $(m)$ = $4 \, kg$Acceleration due to gravity $(g)$ = $3.1\pi \, m/s^2$Formula:$\sigma = \frac{F}{A} = \frac{mg}{\pi r^2}$Calculation:$\sigma = \frac{4 	imes 3.1\pi}{\pi 	imes (2.0 	imes 10^{-3})^2}$$\sigma = \frac{4 	imes 3.1\pi}{\pi 	imes 4.0 	imes 10^{-6}}$$\sigma = \frac{12.4\pi}{4.0\pi 	imes 10^{-6}}$$\sigma = 3.1 	imes 10^6 \, N/m^2$

$A$ steel wire having a radius of $2.0 \, mm$, carrying a load of $4 \, kg$, is hanging from a ceiling. Given that $g = 3.1\pi \, m/s^2$, what will be the tensile stress that would be developed in the wire?

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