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  • A uniform rod of mass m, length L, area of cross-section A and Young's modulus Y hangs from the ceiling. Its elong

A uniform rod of mass m, length L, area of cross-section A and Young's modulus Y hangs from the ceiling. Its elongation under its own weight will be-

Option: 1

Zero


Option: 2

\frac{mgL}{2AY}


Option: 3

\frac{mgL}{AY}


Option: 4

\frac{2mgL}{AY}


Answers (1)

Tension at distance x from the bottom.

\begin{aligned} &\begin{aligned} T & =\left(\frac{m g}{L}\right) \cdot x d t \\ d l & =\frac{T \cdot d x}{A Y} \end{aligned}\\ &\begin{aligned} \therefore \quad \Delta l & =\int_0^L d l \\ \Delta l & =\frac{m g L}{2 A Y} \end{aligned} \end{aligned}

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Kshitij

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