$A$ wire of cross-sectional area $10^{-6} \, m^2$ is stretched such that its length increases by $0.1\%$. If the tension produced in the wire is $1000 \, N$, calculate the Young's modulus of the wire.

If $\delta$ is the depression produced in a beam of length $L$,breadth $b$ and thickness $d$,when a load $W$ is placed at the mid-point,then:

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.

In a tensile test on a metal bar of diameter $0.015 \ m$ and length $0.2 \ m$, the relation between the load and elongation within the proportional limit is found to be $F = 97.2 \times 10^6 (\Delta L)$, where $F$ is the load in $N$ and $\Delta L$ is the elongation in $m$. The Young's modulus of the material in $GPa$ is:

Two wires each of radius $0.2\,cm$ and negligible mass, one made of steel and the other made of brass, are loaded as shown in the figure. The elongation of the steel wire is $.........\times 10^{-6}\,m$. [Young's modulus for steel $= 2 \times 10^{11}\,N/m^2$ and $g = 10\,m/s^2$]

What should be the diameter of a copper wire $(Y=12 \times 10^{10} \text{ N/m}^2)$ of length $5 \text{ m}$ to produce the same elongation produced by a $5 \text{ m}$ long aluminium wire $(Y=7 \times 10^{10} \text{ N/m}^2)$ of diameter $3 \text{ mm}$ with the same $40 \text{ kg}$ mass (in $\text{ mm}$)?