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Specific Heat Capacity

A wire whose ...

Question

A wire whose cross-section area is $4 {m m}^{2}$ is stretched by $0.1 m m$ by a certain weight. How far will a wire of the same material and length stretch, if its cross-sectional area is $8 {m m}^{2}$ and the same weight is attached?

0.5 m m

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1.0 m m

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0.05 m m

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0.06 m m

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Solution

The correct option is C $0.05 m m$
Young's modulus is given by:
$Y = \frac{F L}{A Δ L}$

It remains the same for both cases as it is a property of the material.
$\frac{F L}{A_{1} Δ L_{1}} = \frac{F L}{A_{2} Δ L_{2}}$
$Δ L_{2} = \frac{4}{8} \times 0.1 = 0.05 m m$

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