A metal wire length L, $$cross-sectional$$ area A and Young's modulus Y is stretched by a variable force F. F is varying in such a way that F is always slightly greater than the elastic forces of resistance in the wire. When the elongation in the wire is l, up to this instant

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Infinity Learn · Accepted Answer

In this question, the applied force is not constant. Let us consider at any instant the wire elongates by x. Then work done by F to elongate it more by dx $$isdW=Fdx=YAxLdx$$[x≪L]$$W=$$∫$$0l$$ $$YAxdxL=YAl22LAs$$ internal restoring force and applied force are almost same (equal$$ and $$opposite), numerical value of work done by these two forces would be equal.

A metal wire length L, cross-sectional area A and Young's modulus Y is stretched by a variable force F. F is varying in such a way that F is always slightly greater than the elastic forces of resistance in the wire. When the elongation in the wire is l, up to this instant

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