How much force is required to produce an increase of $0.2\%$ in the length of a brass wire of diameter $0.6\, mm$ (Young’s modulus for brass = $0.9 \times {10^{11}}N/{m^2}$)

Two wires $A$ and $B$ are of same materials. Their lengths are in the ratio $1 : 2$ and diameters are in the ratio $2 : 1$ when stretched by force ${F_A}$ and ${F_B}$ respectively they get equal increase in their lengths. Then the ratio ${F_A}/{F_B}$ should be

One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be____________.

[Area of cross section of wire $=0.005 \mathrm{~cm}^2$, $\mathrm{Y}=2 \times 10^{11}\  \mathrm{Nm}^{-2}$ and $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$

The following four wires are made of same material. Which one will have the largest elongation when subjected to the same tension ?

The ratio of the lengths of two wires $A$ and $B$ of same material is $1 : 2$ and the ratio of their diameter is $2 : 1.$ They are stretched by the same force, then the ratio of increase in length will be

A uniform heavy rod of weight $10\, {kg} {ms}^{-2}$, crosssectional area $100\, {cm}^{2}$ and length $20\, {cm}$ is hanging from a fixed support. Young modulus of the material of the rod is $2 \times 10^{11} \,{Nm}^{-2}$. Neglecting the lateral contraction, find the elongation of rod due to its own weight. (In $\times 10^{-10} {m}$)