$A$ uniform heavy rod of mass $20\,kg$,cross-sectional area $0.4\,m^{2}$,and length $20\,m$ is hanging from a fixed support. Neglecting the lateral contraction,the elongation in the rod due to its own weight is $x \times 10^{-9}\,m$. The value of $x$ is (Given: Young's modulus $Y = 2 \times 10^{11}\,N/m^{2}$ and $g = 10\,m/s^{2}$)

Which of the following curves represents the correct distribution of elongation $(y)$ along a heavy rod under its own weight? ($L$ = length of rod, $x$ = distance of a point from the lower end).

Two wires $A$ and $B$ of the same length are made of the same material. The load $(F)$ vs. elongation $(x)$ graph for these two wires is shown in the figure. Which of the following statement$(s)$ is/are true?

$A$ compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross-section, $Y$ its Young's modulus, and $\alpha$ its coefficient of linear expansion. Then, $F$ is equal to

Two blocks of mass $2 \ kg$ and $4 \ kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The radius of the wire is $4.0 \times 10^{-5} \ m$ and Young's modulus of the metal is $2.0 \times 10^{11} \ N/m^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $g = 10 \ m/s^2$].

The speed of a transverse wave passing through a string of length $50 \; cm$ and mass $10 \; g$ is $60 \; ms^{-1}$. The area of cross-section of the wire is $2.0 \; mm^2$ and its Young's modulus is $1.2 \times 10^{11} \; Nm^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \; m$. The value of $x$ is $...$