$A$ truck is pulling a car out of a ditch by means of a steel cable that is $9.1 \, m$ long and has a radius of $5 \, mm$. When the car just begins to move,the tension in the cable is $800 \, N$. How much has the cable stretched? (Young's modulus for steel is $2 \times 10^{11} \, N/m^2$)

Two wires $A$ and $B$ made of different materials of length $6.0 \ cm$ and $5.4 \ cm$, respectively, and area of cross-sections $3.0 \times 10^{-5} \ m^2$ and $4.5 \times 10^{-5} \ m^2$, respectively, are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x : 3$. The value of $x$ is . . . . . . . . . . .

$A$ metal rod of cross-sectional area $3 \times 10^{-6} \,m^{2}$ is suspended vertically from one end and has a length of $0.4 \,m$ at $100^{\circ} C$. The rod is cooled to $0^{\circ} C$, but prevented from contracting by attaching a mass '$m$' at the lower end. Find the value of '$m$'. (Given: $Y = 10^{11} \,N/m^{2}$, coefficient of linear expansion $\alpha = 10^{-5} /K$, $g = 10 \,m/s^{2}$) (in $\,kg$)

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

The Young's modulus for steel is much more than that for rubber. For the same longitudinal strain,which one will have greater tensile stress?

$A$ wire of cross-sectional area $10^{-6} \, m^2$ is stretched such that its length increases by $0.1\%$. If the tension produced in the wire is $1000 \, N$, calculate the Young's modulus of the wire.