$A$ 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:

$A$ steel rod of length $1\,m$ and cross-sectional area $10^{-4}\,m^2$ is heated from $0^{\circ}C$ to $200^{\circ}C$ without being allowed to extend or bend. The compressive force produced in the rod is $........\times 10^4\,N$. (Given: Young's modulus of steel $Y = 2 \times 10^{11}\,N/m^2$,coefficient of linear expansion $\alpha = 10^{-5}\,K^{-1}$)

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 $Y = 2.0 \times 10^{11} \; \text{Pa}$,$g = 9.8 \; \text{m/s}^2$]

What is the effect of change in temperature on the Young's modulus?

The density of a rubber cord is $d$. $A$ thick rubber cord of length $L$ and cross-sectional area $A$ undergoes elongation under its own weight when suspended vertically. This elongation is proportional to:

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$,the force with which the metal ring expands is