First slide

Elastic Modulie

Question

Two wires are made of the same material and have the same volume. The first' wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by X on applying a force F, how much force is needed to stretch the second wire by the same amount?

Moderate

A

9 F
B

6 F
C

4 F
D

F

Solution

$Y = \frac{Fl}{A ∆ l} ∵ V = Al, so l = \frac{V}{A} So, F = \frac{YA ∆ l}{l} = \frac{{YA}^{2} ∆ l}{V} \infty A^{2} \frac{F_{1}}{F_{2}} = {(\frac{A_{1}}{A_{2}})}^{2} \Rightarrow \frac{F}{F_{2}} = {(\frac{A}{3 A})}^{2} = \frac{1}{9} \Rightarrow F_{2} = 9 F$

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