The ratio of Young's modulus of the material of two wires is $2 : 3.$ If the same stress is applied on both,then the ratio of elastic energy per unit volume will be

Two wires of the same length and same cross-sectional area are suspended as shown in the figure. Their Young's moduli are $Y_1$ and $Y_2$. What is their equivalent Young's modulus?

Two wires $A$ and $B$ made of different materials of length $6.0 \ cm$ and $5.4 \ cm$,respectively,and area of cross-sections $3.0 \times 10^{-5} \ m^2$ and $4.5 \times 10^{-5} \ m^2$,respectively,are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x : 3$. The value of $x$ is . . . . . . . . . . .

$A$ uniform cylindrical rod of length $L$ and radius $r$ is made from a material whose Young's modulus of elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$,its length remains unchanged. The coefficient of volume expansion of the material of the rod is (nearly) equal to:

The dimensions of four wires of the same material are given below. The increase in length is maximum in the wire of

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 ......... $mm$.