When a wire is stretched to double its length. Select the correct statement from the following.

Its radius is halved

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Its strain is unity

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Its stress become equal to its Young's modules

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Young's modulus is equal to twice the elastic energy per unit volume

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Solution

The correct option is B Its strain is unity
Since volume remains constant
hence, $π R_{1}^{2} L_{1} = π R_{2}^{2} L_{2}$
given $L_{2} = 2 L_{1}$
So $R_{1}^{2} L_{1} = R_{2}^{2} 2 L_{1}$
$R_{1} = \sqrt{2} R_{2}$
& strain = $\frac{△ l}{l} = \frac{{2 L}_{1} - L_{1}}{L_{1}} = 1$
hence, its strain is unity.

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