$A$ steel rod has a radius of $10 \,mm$ and a length of $1.0 \,m$. $A$ force stretches it along its length and produces a strain of $0.32 \%$. The Young's modulus of the steel is $2.0 \times 10^{11} \,N/m^2$. What is the magnitude of the force stretching the rod in $kN$?

The unit of Young's modulus is

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.

As shown in the figure,in an experiment to determine Young's modulus of a wire,the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of the wire is $62.8\,cm$ and its diameter is $4\,mm$. The Young's modulus is found to be $x \times 10^4\,N/m^2$. The value of $x$ is

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by forces in the ratio $3: 1$. The ratio of the elastic potential energies stored per unit volume in the wires $A$ and $B$ is

The Young's modulus of a wire is $Y$. If the energy per unit volume is $E$,then the strain will be