Two wires of the same material have lengths in the ratio $1 : 2$ and their radii are in the ratio $1 : \sqrt{2}$. If they are stretched by applying equal forces,the increase in their lengths will be in the ratio:

The Young's modulus of a wire of length $L$ and radius $r$ is $Y \, N/m^2$. What will be the Young's modulus of a wire made of the same material with length $L/2$ and radius $r/2$?

Overall changes in volume and radii of a uniform cylindrical steel wire are $0.2 \%$ and $0.002 \%$ respectively when subjected to some suitable force. Calculate the longitudinal tensile stress acting on the wire. (Given: Young's modulus $Y = 2.0 \times 10^{11} \ N/m^2$)

Two similar wires under the same load yield elongations of $0.1 \ mm$ and $0.05 \ mm$ respectively. If the area of cross-section of the first wire is $4 \ mm^2$,then the area of cross-section of the second wire is..... $mm^2$.

$A$ metal wire of length $L_1$ and area of cross-section $A$ is attached to a rigid support. Another metal wire of length $L_2$ and of the same cross-sectional area is attached to the free end of the first wire. $A$ body of mass $M$ is then suspended from the free end of the second wire. If $Y_1$ and $Y_2$ are the Young's moduli of the wires respectively,the effective force constant of the system of the two wires is:

$A$ 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 ........ $N$.