$A$ wire is loaded by $6 \ kg$ at its one end,the increase in length is $12 \ mm$. If the radius of the wire is doubled and all other magnitudes are unchanged,then the increase in length will be ......... $mm$.

$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

As shown in the figure,in an experiment to determine Young's modulus of a wire,the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of the wire is $62.8\,cm$ and its diameter is $4\,mm$. The Young's modulus is found to be $x \times 10^4\,N/m^2$. The value of $x$ is

$A$ load $W$ produces an extension of $1 \ mm$ in a thread of radius $r$. If the load is increased to $4W$ and the radius is increased to $2r$,while all other factors remain the same,what will be the new extension in $mm$?

$A$ copper wire of length $4.0 \, m$ and area of cross-section $1.2 \, cm^2$ is stretched with a force of $4.8 \times 10^3 \, N$. If Young's modulus for copper is $1.2 \times 10^{11} \, N/m^2$,the increase in the length of the wire will be:

$A$ uniform cylindrical rod of length $L$ and radius $r$ is made from a material whose Young's modulus of elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$,its length remains unchanged. The coefficient of volume expansion of the material of the rod is (nearly) equal to: