$A$ 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 $g = 10\,m/s^{2}$)

What is the velocity of sound in a perfectly rigid rod? Why?

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

$A$ block of mass $2 \ kg$ is tied to one end of a $2 \ m$ long metal wire of $1.0 \ mm^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is $2 \ mm$, the Young's modulus of the metal is (Acceleration due to gravity $= 10 \ ms^{-2}$)

In an experiment,brass and steel wires of length $1\,m$ each with areas of cross-section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support,while the other end is subjected to an elongation. The stress required to produce a total elongation of $0.2\,mm$ is: [Given: Young's Modulus for steel and brass are $120 \times 10^9\,N/m^2$ and $60 \times 10^9\,N/m^2$ respectively]

Two wires of copper having the lengths in the ratio $4:1$ and their radii in the ratio $1:4$ are stretched by the same force. The ratio of longitudinal strain in the two will be