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  4. A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lower end. If its radius is r, its length L and the Young's modulus for the material of the wire is E, the extension is 1. directly proportional to E 2. inversely proportional to r 3. directly proportional to L

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Q. A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lower end. If its radius is $r$, its length $L$ and the Young's modulus for the material of the wire is $E$, the extension is
1. directly proportional to $E$
2. inversely proportional to $r$
3. directly proportional to $L$

Mechanical Properties of Solids

Solution:

As, $E=\frac{F L}{\pi r^{2} \Delta L}$
or $\Delta L=\frac{F L}{\pi r^{2} E}$
Clearly, $\Delta L \propto L$