On applying a stress of $20 \times {10^8}N/{m^2}$ the length of a perfectly elastic wire is doubled. Its Young’s modulus will be

The Young's modulus of a wire of length $L$ and radius $r$ is $Y$ $N/m^2$. If the length and radius are reduced to $L/2$ and $r/2,$ then its Young's modulus will be

One end of a horizontal thick copper wire of length $2 L$ and radius $2 R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by a applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is :

In $CGS$ system, the Young's modulus of a steel wire is $2 \times {10^{12}}$. To double the length of a wire of unit cross-section area, the force required is

A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is

A steel rod of length $1\,m$ and area of cross section $1\,cm^2$ is heated from $0\,^oC$ to $200\,^oC$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,Nm^{-2}$,  $\alpha = 10^{-5} C^{-1})$