The work done per unit volume to stretch a wi | vedclass

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Question

(B) The energy stored per unit volume (work done per unit volume) in a stretched wire is given by the formula: $U = \frac{1}{2} 	imes Y 	imes (	ext

Vedclass · Accepted Answer

$4.5 	imes 10^7\,J/m^3$

Vedclass · Answer

(B) The energy stored per unit volume (work done per unit volume) in a stretched wire is given by the formula: $U = \frac{1}{2} 	imes Y 	imes (	ext{Strain})^2$.Given that the wire is stretched by $1\%$,the strain is $	ext{Strain} = \frac{\Delta L}{L} = \frac{1}{100} = 0.01$.The Young's modulus is $Y = 9 	imes 10^{11}\,N/m^2$.Substituting these values into the formula:$U = \frac{1}{2} 	imes (9 	imes 10^{11}) 	imes (0.01)^2$$U = 4.5 	imes 10^{11} 	imes 10^{-4}$$U = 4.5 	imes 10^7\,J/m^3$.

The work done per unit volume to stretch a wire by $1\%$ of its length,having a cross-sectional area of $1\,mm^2$,is: $[Y = 9 \times 10^{11}\,N/m^2]$

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