$A$ 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 $mm$?

In an experiment to determine the Young's modulus of a wire of length exactly $1\;m$,the extension in the length of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.02\;mm$ when a load of $1\;kg$ is applied. The diameter of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.01\;mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\;N/m^2$. The value of $x$ is (Take $g = 10\;m/s^2$)

Young's modulus of the material of a wire of length $L$ and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and the cross-sectional area is halved,then the Young's modulus will be:

$A$ 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 ......... $mm$.

$A$ metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{\circ} C$. What is the force required to prevent the expansion of the rod lengthwise? ($Y=$ Young's modulus of the material of the rod,$\alpha=$ coefficient of linear expansion of the rod.)

The ratio of Young's modulus of the material of two wires is $2 : 3.$ If the same stress is applied on both,then the ratio of elastic energy per unit volume will be