The ratio of diameters of two wires of same material is $n : 1$. The length of wires are $4\, m$ each. On applying the same load, the increase in length of thin wire will be

A copper wire $(Y = 1 \times 10^{11}\, N/m^2)$ of length $6\, m$ and a steel wire $(Y = 2 \times 10^{11}\, N/m^2)$ of length $4\, m$ each of cross section $10^{-5}\, m^2$ are fastened end to end and stretched by a tension of $100\, N$. The elongation produced in the copper wire is ……… $mm$

A uniform plank of Young’s modulus $Y $ is moved over a smooth horizontal surface by a constant horizontal force $F.$ The area of cross section of the plank is $A.$ The compressive strain on the plank in the direction of the force 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 tension produced in the rod is $……..\times 10^4\,N$ (Given Young's modulus of steel $=2 \times 10^{11}\,Nm ^{-2}$, coefficient of linear expansion $=10^{-5}\, K ^{-1}$.

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