For a solid rod,the Young's modulus of elasticity is $3.2 \times 10^{11} \, N m^{-2}$ and density is $8 \times 10^3 \, kg m^{-3}$. The velocity of longitudinal wave in the rod will be $......... \times 10^{3} \, m s^{-1}$.

One end of a steel rod of radius $10.0 \ mm$ and length $50.0 \ cm$ is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude $10.0 \times \pi \ kN$. This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus $= 2.0 \times 10^{11} \ N/m^2$) (in $mm$)

$A$ steel wire of length $20 \text{ cm}$ and area of cross-section $1 \text{ mm}^2$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \text{C}$ to $20^{\circ} \text{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $\alpha = 1.1 \times 10^{-5} {}^{\circ} \text{C}^{-1}$ and Young's modulus of steel is $Y = 2.0 \times 10^{11} \text{ N/m}^2$. (in $\text{ N}$)

$A$ steel wire of length $L$ and area of cross-section $A$ is suspended from a rigid support. If $Y$ is the Young's modulus of the material of the wire and $\alpha$ is the coefficient of linear expansion,then the increase in tension when the temperature falls by $t^{\circ} C$ is:

How much force is required to produce an increase of $0.2\%$ in the length of a brass wire of diameter $0.6\, mm$ (Young's modulus for brass = $0.9 \times 10^{11} \, N/m^2$)?

$A$ steel rod has a radius of $10 \,mm$ and a length of $1 \,m$. $A$ $80 \,kN$ force stretches it along its length. If the Young's modulus of the rod is $2 \times 10^{11} \,N/m^2$, then the change in length is