$A$ steel rod has a radius of $10 \,mm$ and a length of $1 \,m$. $A$ $80 \,kN$ force stretches it along its length. If the Young's modulus of the rod is $2 \times 10^{11} \,N/m^2$, then the change in length is

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.

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 $= 12 \times 10^{10} \ Nm^{-2}$)

The length of a metallic wire is $l$. The tension in the wire is $T_1$ for length $l_1$ and the tension in the wire is $T_2$ for length $l_2$. Find the original length $l$.

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by forces in the ratio $3: 1$. The ratio of the elastic potential energies stored per unit volume in the wires $A$ and $B$ is

Two similar wires under the same load yield elongations of $0.1 \ mm$ and $0.05 \ mm$ respectively. If the area of cross-section of the first wire is $4 \ mm^2$,then the area of cross-section of the second wire is..... $mm^2$.