First slide

Elastic Modulie

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

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

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

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

$\frac{1}{16} m m$

Solution

$Y = \frac{F l}{a Δ l}$ Y, l and F are constants.
$Δ l \propto \frac{1}{D^{2}}$ $\Rightarrow$ $\frac{Δ l_{2}}{Δ l_{1}} = \frac{D_{1}^{2}}{D_{2}^{2}} = \frac{1}{16}$ $\Rightarrow Δ l_{2} = \frac{1}{16} m m$

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