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

Answer: (D)

Elastic energy per unit volume of wire.
$\mu =\frac{1}{2} \times$ Young's modulus $\times(\text { Strain })^{2}$
$\therefore \frac{u_{1}}{u_{2}}=\left\{\frac{\left(\text { Strain }_{1}\right.}{(\text { Strain })_{2}}\right\}^{2}=\frac{l^{2}}{L^{2}} \times \frac{4 L^{2}}{4 l^{2}}=1: 1$