A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and tw

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A wire elongates by l mm when a load w is hanged from it....

A wire elongates by $l \mathrm{~mm}$ when a load $w$ is hanged from it. If the wire goes over a pulley and two weights $w$ each are hung at the two ends, then the elongation of the wire will be (in $\mathrm{mm}$ ) [2006]
(A) $l$
(B) $2 l$
(C) Zero
(D) $1 / 2$

Key Concepts

Hooke's Law

Hooke's Law states that the extension or compression of an elastic material is proportional to the applied load provided the deformation is within the elastic limit. This relation, expressed as F = kx, where F is the force applied, x is the extension, and k is the elastic constant, is central to understanding how materials stretch under forces.

Uniform Deformation and Elastic Modulus

A uniform wire, when subjected to a force, deforms according to its elastic modulus and geometry, meaning that its extension is uniformly distributed along its length. This ensures that if different segments of the same wire are loaded with the same tension, each segment will extend proportionally to its original length, allowing for the prediction of overall extension when the wire is used in different configurations.

Load Distribution in Multiple Segments

When a wire is configured such that it is divided into segments (for example, going over a pulley with equal loads on both ends), each segment experiences the same tension as a single load case. If the original extension under a single load is known, and the segments are uniform, the overall extension can be determined by summing the extensions of the individual segments, which in symmetrical arrangements often results in the same overall extension as when a single load is applied.

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