For what reasons can the elastic behavior of a solid body be explained?

Consider two wires of the same material having their ratio of radii to be $2:1$. If these two wires are stretched by an equal force,then the ratio of stress produced in them is

If a solid breaks under a pressure greater than $13 \ atm$ and that solid has a specific gravity of $4$,what is the maximum height of a cylinder made from the solid that can be built at the Earth's surface (in $m$)? (Note: $1 \ atm = 10^5 \ Pa$ and take $g = 10 \ m/s^2$.)

$A$ rod of constant cross-section moves towards the right with constant acceleration $a$. The graph of stress versus distance from the left end is shown in the figure. If the density of the material of the rod at cross-section $1$ is $9 \text{ g/cm}^3$,find the density at cross-section $2$ in $\text{g/cm}^3$.

The length of an elastic string is $a$ metres when the longitudinal tension is $4 \ N$ and $b$ metres when the longitudinal tension is $5 \ N$. The length of the string in metres when the longitudinal tension is $9 \ N$ is

The breaking stress for a wire of radius $r$ of a given material is $F \ Nm^{-2}$. The breaking stress for a wire of the same material of radius $2r$ will be: