$A$ cable is cut to half of its original length. What will be the effect on the increase in its length under a given load?

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:

What is the effect of change in temperature on the Young's modulus?

An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is:

What is the Young's modulus and bulk modulus for a perfect rigid body?