$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is:

$A$ steel wire is stretched with a definite load. If the Young's modulus of the wire is $Y$,how can the value of $Y$ be decreased?

Let a steel bar of length $l$,breadth $b$,and depth $d$ be loaded at the centre by a load $W$. Then the sag of bending of the beam is ($Y =$ Young's modulus of the material of steel).

The length of a metal wire is $L$, when it is subjected to tension $T$. If the tension is increased to $T+\Delta T$, the length becomes $L+\Delta L$. The natural length of the wire is

$A$ rigid bar of mass $15 \, kg$ is supported symmetrically by three wires,each $2 \, m$ long. The wires at each end are made of copper,and the middle one is made of steel. The Young's modulus of elasticity for copper and steel are $110 \times 10^9 \, N/m^2$ and $190 \times 10^9 \, N/m^2$ respectively. If each wire is to have the same tension,the ratio of their diameters (diameter of copper wire to diameter of steel wire) will be ............