$A$ rubber cord $10\, m$ long is suspended vertically. How much does it stretch under its own weight? (Density of rubber is $1500\, kg/m^3$,$Y = 5 \times 10^8\, N/m^2$,$g = 10\, m/s^2$)

The area of cross-section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \, m^2$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons,the required area of cross-section of the rope should be $......... \times 10^{-4} \, m^2$ (take $g = 10 \, m/s^2$).

Two different wires made with the same material have their radii in the ratio $1:2$. Their lengths are also in the ratio $1:2$. If the extensions produced are equal when subjected to different loads,find the ratio of the loads applied.

$A$ $14.5\; kg$ mass,fastened to the end of a steel wire of unstretched length $1.0\; m$,is whirled in a vertical circle with an angular velocity of $2\; rev/s$ at the bottom of the circle. The cross-sectional area of the wire is $0.065\; cm^2$. Calculate the elongation of the wire when the mass is at the lowest point of its path.

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

One end of a steel wire of radius $r$ is fixed to a ceiling and a load of $3 \ kg$ is attached to the free end of the wire. Another wire made of copper of radius $2r$ is attached to the bottom of the $3 \ kg$ load and a $2 \ kg$ load is attached to the free end of the copper wire. The ratio of longitudinal strains produced in copper and steel wires is (Young modulus of steel $= 20 \times 10^{10} \ Nm^{-2}$,Young modulus of copper $= 12 \times 10^{10} \ Nm^{-2}$)