$A$ wire of cross-sectional area $10^{-6} \, m^2$ is elongated by $0.1 \%$ when the tension in it is $1000 \, N$. The Young's modulus of the material of the wire is (Assume radius of the wire is constant).

$A$ load of mass $M \ kg$ is suspended from a steel wire of length $2 \ m$ and radius $1.0 \ mm$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0 \ mm$. Now,the load is fully immersed in a liquid of relative density $2$. The relative density of the material of the load is $8$. The new value of increase in length of the steel wire is ........ $mm$.

The maximum elongation of a steel wire of $1 \,m$ length if the elastic limit of steel and its Young's modulus,respectively,are $8 \times 10^8 \,N \,m^{-2}$ and $2 \times 10^{11} \,N \,m^{-2}$,is: (in $\,mm$)

$A$ 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 rod,$\alpha=$ coefficient of linear expansion $]$

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} \; \text{kg}$. The inner and outer radii of each column are $50 \; \text{cm}$ and $100 \; \text{cm}$ respectively. Assuming uniform load distribution,calculate the compressive strain of each column. [Use $Y = 2.0 \times 10^{11} \; \text{Pa}$,$g = 9.8 \; \text{m/s}^2$]

To double the length of an iron wire having $0.5 \, cm^2$ area of cross-section,the required force will be $(Y = 10^{12} \, dyne/cm^2)$.