$A$ constant force is applied to a metal wire of length $L$. The volume of the wire remains constant. The extension produced is proportional to:

If $\rho$ is the density of the material of a wire and $\sigma$ is the breaking stress, what is the greatest length of the wire that can hang freely without breaking?

Same tension is applied to the following four wires made of same material. The elongation is longest in

$A$ wire elongates by $l \ mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$)

At $40\,^oC$,a brass wire of radius $0.5\, mm$ (diameter $1\, mm$) is hung from the ceiling. $A$ small mass $M$ is hung from the free end of the wire. When the wire is cooled down from $40\,^oC$ to $20\,^oC$,it regains its original length of $0.2\, m$. The value of $M$ is close to ........$kg$. (Coefficient of linear expansion $\alpha = 10^{-5}/^oC$ and Young's modulus $Y = 10^{11}\, N/m^2$; $g = 10\, ms^{-2}$)

$A$ copper wire and a steel wire of the same diameter and length are connected end to end and a force is applied,which stretches their combined length by $1 \ cm$. The two wires will have