Question

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 the stored elastic energy per unit volume in the first and second wire is

• A. $1:4$
• B. $1:2$
• C. $2:1$
• D. $1:1$

Answer 1

The correct option is D $1:1$

Elastic energy stored per unit volume is
$\frac{1}{2}\times \sigma \times \epsilon$

$\frac{1}{2}\times Y\times {\epsilon }^2$

${\epsilon }_1=\frac{l}{L}$
${\epsilon }_2=\frac{zl}{\lambda L}=\frac{l}{L}$

$⟹{\epsilon }_1={\epsilon }_2$

So,

$E_1:E_2={\epsilon }_1^2:{\epsilon }_2^2=1:1$