A wire has a cross sectional area ‘A’, length ‘L’ and young’s modulus ‘Y’. It is pulled by a force ‘F’ which causes a total extension of length ‘l’. The force F is so adjusted that the wire is only slowly stretched. Find the work done by the force in pulling the string by a length ‘dx’ when extension is x (0 > x > l).(a) ½*stress*strain*volume(b) (AY/L)xdx(c) F*l(d) ½*stress * strainThis question was addressed to me in an international level competition.Question is from Solids Mechanical Properties in division Mechanical Properties of Solids of Physics – Class 11

A wire has a cross sectional area ‘A’, length ‘L’ and young’

1.	A wire has a cross sectional area ‘A’, length ‘L’ and young’s modulus ‘Y’. It is pulled by a force ‘F’ which causes a total extension of length ‘l’. The force F is so adjusted that the wire is only slowly stretched. Find the work done by the force in pulling the string by a length ‘dx’ when extension is x (0 > x > l).(a) ½stressstrainvolume(b) (AY/L)xdx(c) Fl(d) ½stress strainThis question was addressed to me in an international level competition.Question is from Solids Mechanical Properties in division Mechanical Properties of Solids of Physics – Class 11
Answer» The correct OPTION is (b) (AY/L)xdx For explanation I WOULD say: The force F at any instant will be EQUAL to internal force developed as the wire is to be slowly stretched. ∴ F=(AY/L)x ∴ Work done for dx EXTENSION = F*dx = (AY/L)xdx.

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