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:

Two wires $A$ and $B$ of the same length are made of the same material. The load $(F)$ vs. elongation $(x)$ graph for these two wires is shown in the figure. Which of the following statement$(s)$ is/are true?

The diameter of a brass rod is $4 \ mm$ and Young's modulus of brass is $9 \times 10^{10} \ N/m^2$. The force required to stretch it by $0.1\%$ of its original length is:

$A$ 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 $\text{ N}$)

Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

$A$ wire is stretched $1 \ mm$ by a force $F$. If a second wire of same material,same length and $4$ times the diameter of the first wire is stretched by the same force $F$,then the elongation of the second wire is