$A$ steel rod has a radius of $10 \,mm$ and a length of $1.0 \,m$. $A$ force stretches it along its length and produces a strain of $0.32 \%$. The Young's modulus of the steel is $2.0 \times 10^{11} \,N/m^2$. What is the magnitude of the force stretching the rod in $kN$?

One end of a metal wire is fixed to a ceiling and a load of $2 \ kg$ hangs from the other end. $A$ similar wire is attached to the bottom of the load and another load of $1 \ kg$ hangs from this lower wire. Then the ratio of longitudinal strain of the upper wire to that of the lower wire will be . . . . . . .
[Area of cross section of wire $= 0.005 \ cm^2$,$Y = 2 \times 10^{11} \ Nm^{-2}$ and $g = 10 \ ms^{-2}$]

An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross-section $A$. The Young's modulus of the material of the wire is $Y$. If the mass is pulled down slightly,its frequency of oscillation along the vertical direction is:

Longitudinal stress of $1\,kg/mm^2$ is applied on a wire. The percentage increase in length is $(Y = 10^{11}\,N/m^2)$. (in $\%$)

Four wires of the same material are stretched by the same load. Which one of them will elongate the most if their dimensions are as follows?

$A$ 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 $\text{ N}$)