The length of a metal wire is $L_1$ when the tension is $T_1$ and $L_2$ when the tension is $T_2$. The unstretched length of the wire is:

On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\, mm^2$,the force required is ($Y$ for steel $= 2.2 \times 10^{11}\, N/m^2$).

The density of a rubber cord is $d$. $A$ thick rubber cord of length $L$ and cross-sectional area $A$ undergoes elongation under its own weight when suspended vertically. This elongation is proportional to:

$A$ rod of length $1000\, mm$ and coefficient of linear expansion $\alpha = 10^{-4} / ^\circ C$ is placed symmetrically between fixed walls separated by $1001\, mm$. The Young's modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^\circ C$,then the stress developed in the rod is ........... $MPa$.

Longitudinal stress of $1\,kg/mm^2$ is applied on a wire. The percentage increase in length is $(Y = 10^{11}\,N/m^2)$. (in $\%$)

An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is: