Steel and copper wires of the same length are stretched by the same weight one after the other. The Young's modulus of steel and copper are $2 \times 10^{11} \, N/m^2$ and $1.2 \times 10^{11} \, N/m^2$,respectively. What is the ratio of the increase in their lengths?

$A$ metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{\circ} C$. What is the force required to prevent the expansion of the rod lengthwise? ($Y=$ Young's modulus of the material of the rod,$\alpha=$ coefficient of linear expansion of the rod.)

In steel,the Young's modulus and the strain at the breaking point are $2 \times 10^{11} \, N/m^2$ and $0.15$ respectively. The stress at the breaking point for steel is therefore:

The speed of a transverse wave passing through a string of length $50 \; cm$ and mass $10 \; g$ is $60 \; ms^{-1}$. The area of cross-section of the wire is $2.0 \; mm^2$ and its Young's modulus is $1.2 \times 10^{11} \; Nm^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \; m$. The value of $x$ is $...$

The following four wires are made of the same material. If the same tension is applied to each,the wire having the largest extension is

$A$ $500 \,g$ 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 $= 10 \,m/s^2$)