The mass and length of a wire are $M$ and $L$ respectively. The density of the material of the wire is $d$. On applying a force $F$ on the wire,the increase in length is $l$. Then,the Young's modulus of the material of the wire will be:

If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be

The diameter of a brass rod is $4 \ mm$ and Young's modulus of brass is $9 \times 10^{10} \ N/m^2$. The force required to stretch it by $0.1\%$ of its original length 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 $= 12 \times 10^{10} \ Nm^{-2}$)

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 following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?