Young's moduli of two wires $A$ and $B$ are in the ratio $7 : 4$. Wire $A$ is $2\, m$ long and has radius $R$. Wire $B$ is $1.5\, m$ long and has radius $2\, mm$. If the two wires stretch by the same length for a given load,then the value of $R$ is close to ......... $mm$.

The ratio of the areas of cross-sections of three wires is $1:2:3$ and the ratio of the Young's moduli of their materials is $3:2:1$. If the three wires are of the same length and the same stretching force is applied to the three wires,then the ratio of the elongations of the three wires is

Two wires $A$ and $B$ are made of the same material having a ratio of lengths $\frac{L_A}{L_B} = \frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B} = 2$. If both the wires are stretched using the same force,what would be the ratio of their respective elongations?

Two rods of same material and volume having circular cross-section are subjected to tension $T$. Within the elastic limit,the same force is applied to both the rods. If the diameter of the first rod is half of the second rod,then the ratio of the extension of the first rod to the second rod will be: (in $: 1$)

$A$ metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$,$\alpha$,and $Y$ denote the length of the rod,the coefficient of linear thermal expansion,and the Young's modulus of its material respectively,then for an increase in temperature of the rod by $\Delta T$,the longitudinal stress developed in the rod is

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are the Young's modulus of the materials,then