$A$ wire is loaded by $6 \ kg$ at its one end,the increase in length is $12 \ mm$. If the radius of the wire is doubled and all other magnitudes are unchanged,then the increase in length will be ......... $mm$.

$A$ steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. $A$ force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N/m^2$. The longitudinal strain produced in the wire is $..........\times 10^{-5}$.

The following four wires are made of the same material. If the same tension is applied to each,the wire having the largest extension is

Two wires $A$ and $B$ are stretched by the same force. If,for $A$ and $B$,$Y_A: Y_B = 1: 2$,$r_A: r_B = 3: 1$,and $L_A: L_B = 4: 1$,then the ratio of their extension $\left(\frac{\Delta L_A}{\Delta L_B}\right)$ will be .............

$A$ force of $200\, N$ is applied at one end of a wire of length $2\, m$ and having area of cross-section $10^{-2}\, cm^2$. The other end of the wire is rigidly fixed. If the coefficient of linear expansion of the wire is $\alpha = 8 \times 10^{-6}\, ^\circ C^{-1}$,Young's modulus is $Y = 2.2 \times 10^{11}\, N/m^2$,and its temperature is increased by $5\, ^\circ C$,then the increase in the tension of the wire will be ........ $N$.

$A$ steel rod has a radius of $10 \,mm$ and a length of $1.0 \,m$. $A$ force stretches it along its length and produces a strain of $0.32 \%$. The Young's modulus of the steel is $2.0 \times 10^{11} \,N/m^2$. What is the magnitude of the force stretching the rod in $kN$?