Four wires of same material and of dimensions as under are stretched by a load of same magnitude separately. Which one of them will be elongated maximum?

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Q: 78 (IAS/2007)
Four wires of same material and of dimensions as under are stretched by a load of same magnitude separately.
Which one of them will be elongated maximum?

question_subject: 

Science

question_exam: 

IAS

stats: 

0,10,18,8,6,10,4

keywords: 

{'wires': [0, 0, 1, 1], 'wire': [0, 0, 7, 16], 'mm diameter': [0, 0, 1, 0], 'diameter': [0, 3, 3, 4], 'dimensions': [0, 1, 3, 1], 'same magnitude': [0, 0, 1, 0], 'same material': [0, 0, 2, 4]}

The 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.

Option 1 and 4 have the same length but different diameters. Since diameter is inversely related to elongation, the wire with less diameter (1 mm in option 4) would elongate more.

Option 2 is longer than option 1 but with the same diameter. As length is directly proportional to elongation, the wire in option 2 would elongate more than option 1.

Option 3 has the longest length and the diameter is less than 2mm of option 1 and 2 but more than 1mm of option 4, resulting in a small cross-sectional area. This wire would elongate maximum due to the combined effect of its length and smaller cross-sectional area, making option 3 the correct answer.