$A$ constant force is applied to a metal wire of length $L$. The volume of the wire remains constant. The extension produced is proportional to:

$A$ horizontal steel railroad track has a length of $100 \, m$ when the temperature is $25^{\circ} C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day,when the temperature is $40^{\circ} C$,is ............. $\times 10^7 \, Pa$. (Note: The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5} /^{\circ} C$ and the Young's modulus of steel is $2 \times 10^{11} \, Pa$.)

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by forces in the ratio $3: 1$. The ratio of the elastic potential energies stored per unit volume in the wires $A$ and $B$ is

$A$ steel wire of length $L$ and area of cross-section $A$ is suspended from a rigid support. If $Y$ is the Young's modulus of the material of the wire and $\alpha$ is the coefficient of linear expansion,then the increase in tension when the temperature falls by $t^{\circ} C$ is:

On applying a stress of $20 \times 10^8 \ N/m^2$,the length of a perfectly elastic wire is doubled. Its Young's modulus will be:

$A$ copper wire of length $1.0\, m$ and a steel wire of length $0.5\, m$ having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1\, mm$. If the Young's moduli of copper and steel are respectively $1.0 \times 10^{11}\, N/m^2$ and $2.0 \times 10^{11}\, N/m^2$,the total extension of the composite wire is ........ $mm$.