(i) Prove that the work done in stretching a wire = ½ x tension x extension.
(ii) Prove that the work done per unit volume in stretching a wire for every type of strain = ½ x stress x strain.
(i) Let L be the original length of a wire of cross-section A and Young's modulus Y.
Let the extension in the wire be l.
Let dl be the further extension in the wire. Then, small work done dW in the extension gets stored in the wire and raises its energy.
dW = F dl
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