$A$ wire is stretched $1 \ mm$ by a force $F$. If a second wire of same material,same length and $4$ times the diameter of the first wire is stretched by the same force $F$,then the elongation of the second wire is

$A$ steel wire of length $L$ at $40^{\circ} C$ is suspended from the ceiling and then a mass $m$ is hung from its free end. The wire is cooled down from $40^{\circ} C$ to $30^{\circ} C$ to regain its original length $L$. The coefficient of linear thermal expansion of the steel is $\alpha = 10^{-5} /^{\circ} C$,Young's modulus of steel is $Y = 10^{11} N/m^2$,and the radius of the wire is $r = 1 \ mm$. Assume that $L \gg$ diameter of the wire. Then the value of $m$ in $kg$ is nearly:

Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is $0.5 \ cm$,find the elongation $(l)$ of each wire. Given: ${Y_s} = 2.0 \times {10^{11}} \ N/m^2$ and ${Y_c} = 1.2 \times {10^{11}} \ N/m^2$.

$A$ wire extends by $1 \ mm$ when a force is applied. If double the force is applied to another wire of the same material and length but half the radius of the cross-section,what will be the elongation of the wire in $mm$?

Two wires of equal lengths are made of the same material. Wire $A$ has a diameter that is twice as that of wire $B$. If identical weights are suspended from the ends of these wires,the increase in length is

Four wires of the same material are stretched by the same load. Which one of them will elongate the most if their dimensions are as follows?