When a weight of $10 \,kg$ is suspended from a copper wire of length $3 \,m$ and diameter $0.4 \,mm$, its length increases by $2.4 \,cm$. If the diameter of the wire is doubled, then the extension in its length will be (in $\,cm$)

$A$ $4 \ kg$ stone attached at the end of a steel wire is being whirled at a constant speed $12 \ ms^{-1}$ in a horizontal circle. The wire is $4 \ m$ long with a diameter $2.0 \ mm$ and Young's modulus of the steel is $2 \times 10^{11} \ Nm^{-2}$. The strain in the wire is:

The interatomic distance for a metal is $3 \times 10^{-10} \ m$. If the interatomic force constant is $3.6 \times 10^{-9} \ N/\mathring{A}$,then the Young's modulus in $N/m^2$ will be:

In which case is there maximum extension in the wire,if the same force is applied to each wire?

Two metallic wires $P$ and $Q$ have the same volume and are made up of the same material. If their areas of cross-section are in the ratio $4:1$ and a force $F_1$ is applied to $P$,an extension of $\Delta l$ is produced. The force required to produce the same extension in $Q$ is $F_2$. The value of $\frac{F_1}{F_2}$ is . . . . . . .

Under the same load,wire $A$ having length $5.0 \, m$ and cross-section $2.5 \times 10^{-5} \, m^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \, m$ and a cross-section of $3.0 \times 10^{-5} \, m^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be