Elongation of Hanging Rope under Self-Weight – Rankers Physics

Solids: Practice Problem & Solution

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:
\(\frac{\rho gL}{2Y}\)
\(\frac{\rho gL^2}{2Y}\)
\(\frac{\rho gL^2}{2AY}\)
\(\frac{\rho gL^2}{Y}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:

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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