$A$ wire of length $2 \, m$ is made from copper having a volume of $10 \, cm^3$. When a force $F$ is applied,the extension in its length is $2 \, mm$. If a wire of length $8 \, m$ is made from the same volume of copper,what will be the extension in its length in $cm$ when the same force $F$ is applied?

$A$ rod of length $L$ at room temperature and uniform area of cross section $A$ is made of a metal having a coefficient of linear expansion $\alpha /^{\circ}C$. It is observed that an external compressive force $F$,applied on each of its ends,prevents any change in the length of the rod when its temperature rises by $\Delta T \, K$. The Young's modulus $Y$ for this metal is:

The force required to stretch a steel wire of area of cross-section $1 \,mm^2$ to double its length is (Young's modulus of steel $= 2 \times 10^{11} \,N \,m^{-2}$)

The speed of a transverse wave travelling in a wire of length $50 \text{ cm}$,cross-sectional area $1 \text{ mm}^2$ and mass $5 \text{ g}$ is $80 \text{ ms}^{-1}$. The Young's modulus of the material of the wire is $4 \times 10^{11} \text{ Nm}^{-2}$. The extension in the length of the wire is

$A$ force is applied to a steel wire '$A$',rigidly clamped at one end. As a result,the elongation in the wire is $0.2\,mm$. If the same force is applied to another steel wire '$B$' of double the length and a diameter $2.4$ times that of the wire '$A$',the elongation in the wire '$B$' will be $............\times 10^{-2}\,mm$ (wires having uniform circular cross sections).

$A$ metallic rod having area of cross-section $A$,Young's modulus $Y$,coefficient of linear expansion $\alpha$,and length $L$ is tied between two strong pillars. If the rod is heated through a temperature $t \, ^\circ C$,then how much force is produced in the rod?