when a load is applied to a wire the extension is 3mm . the extention in the wire of same material and length but half the radius extended by same load is

As the extension in wire is given by dl = Fl/Ay. And as it is inversely proportional to area so extension in new write will be 4 times of previous one and will be equal to =4*3mm = 12mm.Hope it clears. If u have doubts then please clearify. And if u like my answer then please approve answer