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A wire of initial length $L$ and raidus $r$ is stretched by a length $l$. Another wire of same material but with initial length $2 L$ and radius $2 r$ is stretched by a length $2 l$. The ratio of stored elastic energy per unit volume in the first and second wire is
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$1: 1$
Elastic energy per unit volume of wire. $\mu=\frac{1}{2} \times$ Young's modulus $\times(\text { Strain })^{2}$
$\therefore \quad \frac{u_{1}}{u_{2}}=\left\{\frac{(\text { Strain })_{1}}{(\text { Strain })_{2}}\right\}^{2}=\frac{l^{2}}{L^{2}} \times \frac{4 L^{2}}{4 l^{2}}=1: 1$
$\therefore \quad \frac{u_{1}}{u_{2}}=\left\{\frac{(\text { Strain })_{1}}{(\text { Strain })_{2}}\right\}^{2}=\frac{l^{2}}{L^{2}} \times \frac{4 L^{2}}{4 l^{2}}=1: 1$
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