Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to the same range of temperatures. If the coefficient of linear expansion of $A$ is $\frac{3}{2}$ times that of $B$, then the ratio of the thermal stresses produced in the two wires $A$ and $B$ is

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

$A$ uniform cylindrical rod of length $L$ and radius $r$ is made from a material whose Young's modulus of elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$,its length remains unchanged. The coefficient of volume expansion of the material of the rod is (nearly) equal to:

What force is required to increase the length of a wire of diameter $4 \, mm$ and Young's modulus $9 \times 10^{10} \, N/m^2$ by $0.1\%$?

The figure represents the extension $(\Delta l)$ of a wire of length $1\text{ m}$, suspended from the ceiling of a room at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-5}\text{ m}^2$, then the Young's modulus of the wire is . . . . . . $\text{N/m}^2$.

$A$ piece of copper having a rectangular cross-section of $15.2 \; mm \times 19.1 \; mm$ is pulled in tension with $44,500 \; N$ force,producing only elastic deformation. Calculate the resulting strain.