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:

The units of Young's modulus of elasticity are

If $\rho$ is the density of the material of a wire and $\sigma$ is the breaking stress, what is the greatest length of the wire that can hang freely without breaking?

There are two wires of the same material and same length. The diameter of the second wire is two times the diameter of the first wire. What is the ratio of the extensions produced in the wires by applying the same load?

The unit of Young's modulus is

$A$ steel rod of length $1\,m$ and cross-sectional area $10^{-4}\,m^2$ is heated from $0^{\circ}C$ to $200^{\circ}C$ without being allowed to extend or bend. The compressive force produced in the rod is $........\times 10^4\,N$. (Given: Young's modulus of steel $Y = 2 \times 10^{11}\,N/m^2$,coefficient of linear expansion $\alpha = 10^{-5}\,K^{-1}$)