Four wires of the same material and of dimensions as under are stretched by a load of the same magnitude separately. Which one of them will be elongated maximum?
✓ Correct answer: c) Wire of 3 m length and 1.5 mm diameter
ExplanationThe elongation of a wire under a load depends on its length, cross-sectional area and the material of the wire.In this case, all four wires are made of the same material, which means that the material`s properties will not be a factor in determining the elongation.The elongation (ΔL) of a wire under a given load is determined by Hooke’s Law and is given by the formula: ΔL = F⋅L/A⋅Y F: Force applied (which is same for all wires) L: Length of the wire A: cross sectional area of the wire (depends on diameter (d), i.e. (πd2/4)) Y: Young’s modulus of the material (same for all the wires) On substituting the values ; elongation (ΔL) ∝ L/d2 The elongation is proportional to L/d2, and the wire with the highest value of L/d2 will elongate the most, which comes out to be for the wire with length 3m and diameter 1.5mm.214
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