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

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 cross-sectional areas of steel and brass wires are $0.1 \,cm^2$ and $0.2 \,cm^2$ respectively. If the same stress is produced in both by a weight $W$,what is the ratio of the tensions $T_1/T_2$?

When a force $F_1$ is applied on a metallic wire,the length of the wire is $L_1$. If a force $F_2$ is applied on the same wire,the length of the wire is $L_2$. The original length of the wire $L$ is

According to $C.E.$ van der Waals,the interatomic potential varies with the average interatomic distance $(R)$ as

$A$ rod is placed on a smooth horizontal surface. What is the stress developed when the temperature is increased by $40\,^{\circ}C$?
$[\alpha = 5\, \times\, 10^{-5}\,^{\circ}C^{-1},\, Y = 5\, \times\, 10^{11}\, N/m^2]$