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  4. A wire is stretched by 1 mm by a force of 1 kN. How long would a wire of same material and length but of four times radius be stretched by same force.

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Q. A wire is stretched by $1\, mm$ by a force of $1\, kN$. How long would a wire of same material and length but of four times radius be stretched by same force.

Solution:

$\frac{F}{a}=Y \cdot \frac{\Delta L}{L}$
$\Delta L=\frac{F L}{Y a}$
$\therefore \Delta L \propto \frac{1}{a}(F, Y=$ const. $)$
$\frac{\Delta L'}{\Delta L}=\frac{a}{a'}=\left[\frac{\pi r^{2}}{\pi(4 r)^{2}}\right]$
$=\frac{1}{16} mm$