$A$ steel ring of radius $r$ and cross-section area $A$ is fitted onto a wooden disc of radius $R$ $(R > r)$. If Young's modulus is $E$,then the force with which the steel ring is expanded is

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.

The Young's modulus of a wire is $Y$. If the energy per unit volume is $E$,then the strain will be

$A$ wire of area of cross-section $10^{-6} \ m^2$ is increased in length by $0.1 \%$. The tension produced is $1000 \ N$. The Young's modulus of the wire 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 $= 10 \,m/s^2$)

The ratio of the areas of cross-sections of three wires is $1:2:3$ and the ratio of the Young's moduli of their materials is $3:2:1$. If the three wires are of the same length and the same stretching force is applied to the three wires,then the ratio of the elongations of the three wires is