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  4. A uniform wire 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

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Q. A uniform wire 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

Mechanical Properties of Solids

Solution:

In case of elongation by its own weight $mg$ will act at centre of gravity of the wire so that length of wire which is stretched will be $\left(\frac{L}{2}\right)$.
$\therefore \Delta L=\frac{(m g)\left(\frac{L}{2}\right)}{A Y}$
$=\frac{m g L}{2 A Y}$