Question

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 * strain

This 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 1

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.