$A$ 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?

In an experiment to determine the Young's modulus of a wire of length exactly $1\;m$,the extension in the length of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.02\;mm$ when a load of $1\;kg$ is applied. The diameter of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.01\;mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\;N/m^2$. The value of $x$ is (Take $g = 10\;m/s^2$)

Which one of the following is not a unit of Young's modulus?

Two wires $A$ and $B$ of the same cross-section are connected end to end. When the same tension is applied to both wires,the elongation in wire $B$ is twice the elongation in wire $A$. If $L_A$ and $L_B$ are the initial lengths of the wires $A$ and $B$ respectively,then (Young's modulus of material of wire $A = 2 \times 10^{11} \ Nm^{-2}$ and Young's modulus of material of wire $B = 1.1 \times 10^{11} \ Nm^{-2}$):

$A$ metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. $A$ second block having mass $2M$ is suspended at the bottom of the first block using a string $B$. The area of cross-sections of strings $A$ and $B$ are the same. The ratio of lengths of strings $A$ to $B$ is $2$ and the ratio of their Young's moduli $(Y_A/Y_B)$ is $0.5$. The ratio of elongations in $A$ to $B$ is . . . . . . .

$A$ rigid bar of mass $15 \, kg$ is supported symmetrically by three wires,each $2 \, m$ long. The wires at each end are made of copper,and the middle one is made of steel. The Young's modulus of elasticity for copper and steel are $110 \times 10^9 \, N/m^2$ and $190 \times 10^9 \, N/m^2$ respectively. If each wire is to have the same tension,the ratio of their diameters (diameter of copper wire to diameter of steel wire) will be ............