Elongation of Hanging Rope under Self-Weight – Rankers Physics
Topic: Solid and Fluids
Subtopic: Solids

Elongation of Hanging Rope under Self-Weight

A uniform rope of density \(rho\) and length \(L\) is hanging from roof. If young's modulus of material of rope is \(Y\), then elongation produced in rope due to its own weight is:
\(\frac{\rho gL}{2Y}\)
\(\frac{\rho gL^2}{2Y}\)
\(\frac{\rho gL^2}{2AY}\)
\(\frac{\rho gL^2}{Y}\)

Solution:

The elongation of a uniform rope under its own weight is given by \(\Delta L = \frac{MgL}{2AY}\). Substituting mass \(M = \rho A L\), we obtain \(\Delta L = \frac{\rho g L^2}{2Y}\).

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