Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$,while their areas of cross-section are in the ratio of $1: 3$. If the same amount of load is applied to both the wires,the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of [Assume length of wires $A$ and $B$ are same].

$A$ 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?

In an experiment,brass and steel wires of length $1\,m$ each with areas of cross-section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support,while the other end is subjected to an elongation. The stress required to produce a total elongation of $0.2\,mm$ is: [Given: Young's Modulus for steel and brass are $120 \times 10^9\,N/m^2$ and $60 \times 10^9\,N/m^2$ respectively]

$A$ copper wire $(Y = 1 \times 10^{11} \, N/m^2)$ of length $6 \, m$ and a steel wire $(Y = 2 \times 10^{11} \, N/m^2)$ of length $4 \, m$,each of cross-sectional area $10^{-5} \, m^2$,are fastened end to end and stretched by a tension of $100 \, N$. The elongation produced in the copper wire is ......... $mm$.

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

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$