When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end,its length increases by $l$. If the radius of the wire and the applied force were halved,then the increase in its length is

$A$ ring of a thin wire of cross-sectional area $a$ and length $l$ is dipped into a liquid of surface tension $\sigma$ and taken out so that a film of liquid is formed in the ring. If Young's modulus of the material of the wire is $Y$,then the longitudinal strain developed in the ring will be:

$A$ wire of cross-sectional area $3 \, mm^2$ is first stretched between two fixed points at a temperature of $20^{\circ}C$. Determine the tension in the wire when the temperature falls to $10^{\circ}C$. Given: Coefficient of linear expansion $\alpha = 10^{-5} \, ^{\circ}C^{-1}$ and Young's modulus $Y = 2 \times 10^{11} \, N/m^2$.

$A$ steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5}\; m^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

$A$ wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$,its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant,the increase in length will become.

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