Two wires of the same material have lengths in the ratio $1 : 2$ and their radii are in the ratio $1 : \sqrt{2}$. If they are stretched by applying equal forces,the increase in their lengths will be in the ratio:

$A$ cable is cut to half of its original length. What will be the effect on the increase in its length under a given load?

$A$ metal rod of Young's modulus $Y$ and coefficient of linear expansion $\alpha$ has its temperature raised by $\Delta \theta$. The linear stress required to prevent the expansion of the rod is:

Two rods of different materials having coefficients of linear expansion $\alpha_1, \alpha_2$ and Young's moduli $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1 : \alpha_2 = 2 : 3$,and the thermal stresses developed in the two rods are equal,then the ratio $Y_1 : Y_2$ is equal to:

$A$ steel wire of length $20 \text{ cm}$ and area of cross-section $1 \text{ mm}^2$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \text{C}$ to $20^{\circ} \text{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $\alpha = 1.1 \times 10^{-5} {}^{\circ} \text{C}^{-1}$ and Young's modulus of steel is $Y = 2.0 \times 10^{11} \text{ N/m}^2$. (in $\text{ N}$)

An iron rod of length $2\, m$ and cross-sectional area of $50\, mm^2$ is stretched by $0.5\, mm$ when a mass of $250\, kg$ is hung from its lower end. The Young's modulus of the iron rod is: