The area of cross-section of a wire of length $1.1 \, m$ is $1 \, mm^2$. It is loaded with $1 \, kg$. If Young's modulus of copper is $1.1 \times 10^{11} \, N/m^2$,then the increase in length will be ......... $mm$ (Take $g = 10 \, m/s^2$)

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 $......... \times 10^{3} \, m s^{-1}$.

In which case is there maximum extension in the wire,if the same force is applied to each wire?

Two separate wires $A$ and $B$ are stretched by $2 \, mm$ and $4 \, mm$ respectively,when they are subjected to a force of $2 \, N$. Assume that both the wires are made up of the same material and the radius of wire $B$ is $4$ times that of the radius of wire $A$. The lengths of the wires $A$ and $B$ are in the ratio of $a : b$. Then $a / b$ can be expressed as $1 / x$ where $x$ is:

$A$ metallic rod having area of cross-section $A$,Young's modulus $Y$,coefficient of linear expansion $\alpha$,and length $L$ is tied between two strong pillars. If the rod is heated through a temperature $t \, ^\circ C$,then how much force is produced in the rod?

$A$ $500 \,g$ ball is attached to one end of an aluminum wire of area of cross-section $0.5 \,mm^2$ and an unstretched length of $1.4 \,m$. The other end of the wire is fixed to the top of a vertical pole. The ball rotates about the pole in a horizontal plane such that the angle between the wire and the horizontal is $30^{\circ}$. The increase in the length of the wire is . . . . . . $mm$. (Young's modulus of aluminum $= 0.7 \times 10^{11} \,N/m^2$ and acceleration due to gravity $= 10 \,m/s^2$)