The work done in increasing the length of a $1 \, m$ long wire of cross-sectional area $1 \, mm^2$ by $1 \, mm$ is (Given $Y = 2 \times 10^{11} \, N/m^2$): (in $, J$)

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4$,the ratio of their diameters is

$A$ copper wire of length $3 \text{ m}$ is stretched by $3 \text{ mm}$ by applying an external force. The volume of the wire is $600 \times 10^{-6} \text{ m}^3$. The elastic potential energy stored in the wire in the stretched condition is . . . . . . $\text{J}$. (Given Young's modulus of copper $Y = 1.1 \times 10^{11} \text{ N/m}^2$)

$A$ wire of length $50\, cm$ and cross-sectional area of $1\, mm^2$ is extended by $1\, mm$. The required work done will be $(Y = 2 \times 10^{10}\, N/m^2)$.

The work done in increasing the length of a $1 \ m$ long wire of cross-section area $1 \ mm^2$ by $1 \ mm$ will be ....... $J$ $(Y = 2 \times 10^{11} \ Nm^{-2})$

$A$ 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