$A$ force $F$ is applied to a wire of length $L$ and radius $r$,resulting in an extension $l$. What will be the extension in a wire of length $2L$ and radius $2r$ when a force $2F$ is applied?

If the density of the material increases,the value of Young's modulus

When a force of $4 \, N$ is applied to a wire,its length is $a \, m$. When a force of $5 \, N$ is applied,its length is $b \, m$. What will be its length when a force of $9 \, N$ is applied?

When a rod is heated but prevented from expanding,the stress developed is independent of

The area of cross-section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \, m^2$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons,the required area of cross-section of the rope should be $......... \times 10^{-4} \, m^2$ (take $g = 10 \, m/s^2$).

$A$ stretched wire of a material whose Young's modulus $Y = 2 \times 10^{11} \ Nm^{-2}$ has Poisson's ratio $\sigma = 0.25$. Its lateral strain is $\varepsilon_l = 10^{-3}$. The elastic energy density of the wire is: