The unit of Young's modulus is

$A$ wire of length $L$ and area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when a mass $M$ is suspended from its free end. The expression for Young's modulus 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

$A$ metallic rod breaks when the strain produced is $0.2 \%$. The Young's modulus of the material of the rod is $7 \times 10^9 \,N/m^2$. The area of cross-section required to support a load of $10^4 \,N$ is:

Two wires of different materials have same length $L$ and same diameter $d$. The second wire is connected at the end of the first wire and forms one single wire of double the length. This wire is subjected to a stretching force $F$ to produce an elongation $\ell$. The two wires have:

Two wires of diameter $0.25 \; cm,$ one made of steel and the other made of brass,are loaded as shown in the figure. The unloaded length of the steel wire is $1.5 \; m$ and that of the brass wire is $1.0 \; m.$ Compute the elongations of the steel and the brass wires. (Given: Young's modulus of steel $Y_s = 2.0 \times 10^{11} \; Pa,$ Young's modulus of brass $Y_b = 0.91 \times 10^{11} \; Pa$)