First slide

Elastic behaviour of solids

Question

A wire is stretched 1 mm by a force of 1 kN How far would a wire of the same material and length but of four times that diameter be stretched by the same force?

Moderate

A

$\frac{1}{2} mm$
B

$\frac{1}{4} mm$
C

$\frac{1}{8} mm$
D

$\frac{1}{16} mm$

Solution

$Y = \frac{Fl}{aΔl}$
Y, I and F are constants.
$\begin{array}{l} ∴ Δl \propto \frac{1}{D^{2}} \\ \frac{{Δl}_{2}}{{Δl}_{1}} = \frac{D_{1}^{2}}{D_{2}^{2}} = \frac{1}{16} \\ ∴ {Δl}_{2} = \frac{1}{16} mm \end{array}$

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