The diameter of a brass rod is $4 \ mm$ and Young's modulus of brass is $9 \times 10^{10} \ N/m^2$. The force required to stretch it by $0.1\%$ of its original length is:

Why are springs made of steel instead of copper?

$A$ steel rod with $Y = 2.0 \times 10^{11} \, N/m^2$ and $\alpha = 10^{-5} \, ^\circ C^{-1}$ of length $4 \, m$ and area of cross-section $10 \, cm^2$ is heated from $0^\circ C$ to $400^\circ C$ without being allowed to extend. The tension produced in the rod is $x \times 10^5 \, N$ where the value of $x$ is ....... .

$A$ uniform heavy rod of mass $20\,kg$,cross-sectional area $0.4\,m^{2}$,and length $20\,m$ is hanging from a fixed support. Neglecting the lateral contraction,the elongation in the rod due to its own weight is $x \times 10^{-9}\,m$. The value of $x$ is (Given: Young's modulus $Y = 2 \times 10^{11}\,N/m^{2}$ and $g = 10\,m/s^{2}$)

Two wires made of the same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If $x$ is the increase in the length of the first wire,then the increase in the length of the second wire is

$A$ load of mass $M \ kg$ is suspended from a steel wire of length $2 \ m$ and radius $1.0 \ mm$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0 \ mm$. Now,the load is fully immersed in a liquid of relative density $2$. The relative density of the material of the load is $8$. The new value of increase in length of the steel wire is ........ $mm$.