The work done per unit volume in stretching a | vedclass

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(A) The work done by the external applied force during stretching is stored as potential energy $(U)$ in the wire,which is known as strain energy.The

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$\frac{1}{2} 	imes 	ext{stress} 	imes 	ext{strain}$

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(A) The work done by the external applied force during stretching is stored as potential energy $(U)$ in the wire,which is known as strain energy.The work done $W$ is given by the area under the force-extension graph,which is $W = \frac{1}{2} 	imes F 	imes l$,where $F$ is the load and $l$ is the extension.To find the work done per unit volume,we divide the total energy by the volume of the wire $(V = A 	imes L)$,where $A$ is the cross-sectional area and $L$ is the original length.$	ext{Energy per unit volume} = \frac{U}{V} = \frac{\frac{1}{2} F l}{A L}$Rearranging the terms,we get:$\frac{U}{V} = \frac{1}{2} 	imes \left( \frac{F}{A} ight) 	imes \left( \frac{l}{L} ight)$Since $	ext{stress} = \frac{F}{A}$ and $	ext{strain} = \frac{l}{L}$,the expression becomes:$	ext{Strain energy per unit volume} = \frac{1}{2} 	imes 	ext{stress} 	imes 	ext{strain}$.

The work done per unit volume in stretching a wire is :-

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