$A$ uniform dense rod with non-uniform Young's modulus is hanging from the ceiling under gravity. If the elastic energy density at every point is the same,then how will Young's modulus change with $x$ as shown in the graphs?

$A$ block of weight $100 \ N$ is suspended by copper and steel wires of same cross-sectional area $0.5 \ cm^2$ and lengths $\sqrt{3} \ m$ and $1 \ m$,respectively. Their other ends are fixed on a ceiling as shown in the figure. The angles subtended by the copper and steel wires with the ceiling are $30^{\circ}$ and $60^{\circ}$,respectively. If the elongation in the copper wire is $\Delta \ell_C$ and the elongation in the steel wire is $\Delta \ell_S$,then the ratio $\frac{\Delta \ell_C}{\Delta \ell_S}$ is. . . . . .
[Young's modulus for copper and steel are $1 \times 10^{11} \ N/m^2$ and $2 \times 10^{11} \ N/m^2$ respectively]

$A$ steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5}\; m^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm^2$ is $2 \times 10^{11}\,N/m^2$. The wire is suspended from its support on a given planet. $A$ block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the Earth. The elongation of the wire is (Take $g$ on the Earth $= 10\,m/s^2$):

$A$ copper wire of length $1.0\, m$ and a steel wire of length $0.5\, m$ having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1\, mm$. If the Young's moduli of copper and steel are respectively $1.0 \times 10^{11}\, N/m^2$ and $2.0 \times 10^{11}\, N/m^2$,the total extension of the composite wire is ........ $mm$.

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?