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?

$A$ copper wire and an aluminium wire have lengths in the ratio $5: 2$, diameters in the ratio $4: 3$ and forces applied in the ratio $4: 5$. Find the ratio of increase in length of the copper wire to that of the aluminium wire. (Given: $Y_{Cu} = 1.1 \times 10^{11} \text{ Nm}^{-2}$, $Y_{Al} = 0.7 \times 10^{11} \text{ Nm}^{-2}$)

The length of a metal wire is found to be $L_1$ and $L_2$ when the tensions $T_1$ and $T_2$ are applied to it respectively. The natural length of the wire is

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

$A$ uniform heavy rod of mass $20\,kg$,cross-sectional area $0.4\,m^{2}$,and length $20\,m$ is hanging from a fixed support. Neglecting the lateral contraction,the elongation in the rod due to its own weight is $x \times 10^{-9}\,m$. The value of $x$ is (Given: Young's modulus $Y = 2 \times 10^{11}\,N/m^{2}$ and $g = 10\,m/s^{2}$)

$A$ load of $2 \,kg$ produces an extension of $1 \,mm$ in a wire of $3 \,m$ in length and $1 \,mm$ in diameter. The Young's modulus of the wire will be .......... $Nm^{-2}$.