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

$A$ steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5}\; m^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

For a solid rod,the Young's modulus of elasticity is $3.2 \times 10^{11} \, N m^{-2}$ and density is $8 \times 10^3 \, kg m^{-3}$. The velocity of longitudinal wave in the rod will be $......... \times 10^{3} \, m s^{-1}$.

Two wires made of the same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If $x$ is the increase in the length of the first wire,then the increase in the length of the second wire is

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} \; \text{kg}$. The inner and outer radii of each column are $50 \; \text{cm}$ and $100 \; \text{cm}$ respectively. Assuming uniform load distribution,calculate the compressive strain of each column. [Use $Y = 2.0 \times 10^{11} \; \text{Pa}$,$g = 9.8 \; \text{m/s}^2$]

If the length of a wire is made double and the radius is halved of its respective values,then the Young's modulus of the material of the wire will: