If the interatomic spacing in a steel wire is $3.0 \mathring{A}$ and $Y_{\text{steel}} = 20 \times 10^{10} \text{ N/m}^2$, then the force constant is:

$A$ brass wire of length $2 \ m$ and radius $1 \ mm$ at $27 ^\circ C$ is held taut between two rigid supports. Initially,it was cooled to a temperature of $-43 ^\circ C$,creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4 \ T$ is . . . . . . $^\circ C$.

The cross-sectional area of each wire is $10^{-4} \, m^2$. What is the displacement of point $B$?

An iron rod of length $2\, m$ and cross-sectional area of $50\, mm^2$ is stretched by $0.5\, mm$ when a mass of $250\, kg$ is hung from its lower end. The Young's modulus of the iron rod is:

$A$ copper wire of length $2.4 \ m$ and an aluminum wire of length $0.7 \ m$, both having diameter $2 \ mm$, are connected end to end. When stretched by a load, the total elongation is found to be $0.6 \ mm$. The applied load is (Young's modulus of copper $= 1.2 \times 10^{11} \ N/m^2$ and Young's modulus of aluminum $= 0.7 \times 10^{11} \ N/m^2$). (in $\pi \ N$)

$A$ steel ring of radius '$r$' is to be fitted over a wooden disc of radius '$R$' $(R > r)$. The force required to expand the ring so that it fits over the disc is ($Y =$ Young's modulus of steel,$A =$ area of cross-section of the wire).