Which of the following curve represents the correctly distribution of elongation $(y)$ along heavy rod under its own weight $L \rightarrow$ length of rod, $x \rightarrow$ distance of point from lower end?

A $5\, m$ long aluminium wire ($Y = 7 \times {10^{10}}N/{m^2})$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times {10^{10}}N/{m^2})$ of the same length under the same weight, the diameter should now be, in $mm.$

Young's modules of material of a wire of length ' $L$ ' and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's $modules$ will be :

A composite rod made up of two rods $AB$ and $BC$ are joined at $B$ . The rods are of equal length at room temperature and have equal masses. The coefficient of linear expansion a of $AB$ is more than that of $BC$. The composite rod is suspended horizontal by means of a thread at $B$. When the rod is heated

A force is applied to a steel wire ' $A$ ', rigidly clamped at one end. As a result elongation in the wire is $0.2\,mm$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be $…………\times 10^{-2}\,mm$ (wires having uniform circular cross sections)