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(D) The elastic potential energy per unit volume $(u)$ of a stretched wire is given by the formula: $u = \frac{1}{2} 	imes Y 	imes (	ext{strain})^2

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$1: 1$

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(D) The elastic potential energy per unit volume $(u)$ of a stretched wire is given by the formula: $u = \frac{1}{2} 	imes Y 	imes (	ext{strain})^2$,where $Y$ is Young's modulus and $	ext{strain} = \frac{\Delta L}{L}$.For the first wire: $	ext{strain}_1 = \frac{l}{L}$.Thus,$u_1 = \frac{1}{2} Y (\frac{l}{L})^2$.For the second wire: $	ext{strain}_2 = \frac{2l}{2L} = \frac{l}{L}$.Thus,$u_2 = \frac{1}{2} Y (\frac{l}{L})^2$.Since both wires are made of the same material,their Young's modulus $Y$ is the same.The ratio of the stored elastic energy per unit volume is $\frac{u_1}{u_2} = \frac{\frac{1}{2} Y (l/L)^2}{\frac{1}{2} Y (l/L)^2} = 1:1$.

$A$ wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of stored elastic energy per unit volume in the first and second wire is

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