Variation of Longitudinal Strain With Longitudinal Stress

Springs are made of steel and not of copper.

A steel wire of length $1 \mathrm{m}$ and diameter $3 \mathrm{mm}$ is stretched horizontally between supports attached at its ends. What load hung from the mid-point of the wire would be required to produce a depression of $1 \mathrm{cm}$? $\left(Y=2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2, g=9.8 \mathrm{m}/{\mathrm{s}}^2\right)$.

A wire of length $1 \mathrm{m}$ and radius $1 \mathrm{mm}$ is welded to another wire of length $2 \mathrm{m}$ and radius $2 \mathrm{mm}$. The free end of the first is clamped and a load of $5 \mathrm{kg}$ is applied at the free end of the second wire. What is the total increase of compound wire? ($Y$ of both wire$=2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$).

A steel wire of $2 \mathrm{mm}$ diameter is just stretched between two points at a temperature of $25°C$. Determine the tension when the temperature falls to $15°C$ (linear expansively of steel$=11\times {10}^{-6}l° \mathrm{K}, {\mathrm{Y}}_{\mathrm{steel}}=2.1\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$).

A wire of length $3 \mathrm{m}$, diameter $0.4 \mathrm{mm}$ and Young's modulus $8\times {10}^{10} \mathrm{N}/{\mathrm{m}}^2$, is suspended from a point and supports a heavy cylinder of volume ${10}^{-3} {\mathrm{m}}^3$; at its lower end. Find the decrease in length when the metal cylinder is immersed in a liquid of density $800 \mathrm{kg}/{\mathrm{m}}^3$.

A copper wire of $2.0 \mathrm{m}$ long and $0.5 \mathrm{mm}$ in diameter supports a mass of $10 \mathrm{kg}$. It is stretched by $2.38 \mathrm{mm}$. Calculate Young's modulus of the wire.

Two wires of same material and same radius are stretched by equal forces. Find the ratio of their elongation if their lengths are in the ratio $1:2$.

A steel rail $100 \mathrm{m}$ long and $40 {\mathrm{cm}}^2$ in area of cross-section changes in length by $1 \mathrm{cm}$, then calculate tension developed in the rail? If young's modulus of the steel is $2\times {10}^{11}\mathrm{N}/{\mathrm{m}}^2$.