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Longitudinal Strain

A wire whose ...

Question

A wire whose cross-sectional area is $A_{1}$ is stretched by distance $Δ L_{1}$ by a certain weight. How far will a wire of the same material and same length and cross-sectional area $A_{2}$ stretch, if the same weight is applied to it?

\frac{A_{1} Δ L_{1}}{A_{2}}

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Δ L_{1}

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\frac{A_{2} Δ L_{1}}{A_{1}}

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None of these

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Solution

The correct option is A $\frac{A_{1} Δ L_{1}}{A_{2}}$
We know from Hooke's law that
$Δ L = \frac{F L}{A Y}$
Or $A Δ L = \frac{F L}{Y}$

As $F$ , $L$ and $Y$ are same, so $A Δ L = constant$
or $A_{1} Δ L_{1} = A_{2} Δ L_{2}$
or $Δ L_{2} = \frac{A_{1} Δ L_{1}}{A_{2}}$

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