$A$ $4 \ kg$ stone attached at the end of a steel wire is being whirled at a constant speed $12 \ ms^{-1}$ in a horizontal circle. The wire is $4 \ m$ long with a diameter $2.0 \ mm$ and Young's modulus of the steel is $2 \times 10^{11} \ Nm^{-2}$. The strain in the wire is:

The force required to stretch a steel wire of $1\,cm^2$ cross-section to $1.1$ times its original length is $(Y = 2 \times 10^{11}\,N/m^2)$.

In an experiment to determine the Young's modulus,steel wires of five different lengths $(1, 2, 3, 4$ and $5\,m)$ but of same cross-section $(2\,mm^2)$ were taken and curves between extension and load were obtained. The slope $(\text{extension/load})$ of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,N/m^2$,then the value of $x$ is

The dimensions of four wires of the same material are given below. In which wire will the increase in length be maximum when the same tension is applied?

The Young's modulus of a wire of length $L$ and radius $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$,then the Young's modulus will be

$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.