On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\, mm^2$,the force required is ($Y$ for steel $= 2.2 \times 10^{11}\, N/m^2$).

In the $CGS$ system,the Young's modulus of a steel wire is $2 \times 10^{12} \text{ dyn/cm}^2$. To double the length of a wire of unit cross-sectional area,the force required is:

$A$ 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.)

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 speed of a transverse wave passing through a string of length $50 \; cm$ and mass $10 \; g$ is $60 \; ms^{-1}$. The area of cross-section of the wire is $2.0 \; mm^2$ and its Young's modulus is $1.2 \times 10^{11} \; Nm^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \; m$. The value of $x$ is $...$

The mass and length of a wire are $M$ and $L$ respectively. The density of the material of the wire is $d$. On applying a force $F$ on the wire,the increase in length is $l$. Then,the Young's modulus of the material of the wire will be: