The length of an iron wire is $L$ and area of cross-section is $A$. The increase in length is $l$ on applying the force $F$ on its two ends. Which of the statement is correct

A rod $BC$ of negligible mass fixed at end $B$ and connected to a spring at its natural length having spring constant $K = 10^4\  N/m$ at end $C$, as shown in figure. For the rod $BC$ length $L = 4\ m$, area of cross-section $A = 4 × 10^{-4}\   m^2$, Young's modulus $Y = 10^{11} \ N/m^2$ and coefficient of linear expansion $\alpha = 2.2 × 10^{-4} K^{-1}.$ If the rod $BC$ is cooled from temperature $100^oC$  to $0^oC,$ then find the decrease in length of rod in centimeter.(closest to the integer)

A force of ${10^3}$ newton stretches the length of a hanging wire by $1$ millimetre. The force required to stretch a wire of same material and length but having four times the diameter by $1$ millimetre is

A $100\,m$ long wire having cross-sectional area $6.25 \times 10^{-4}\,m ^2$ and Young's modulus is $10^{10}\,Nm ^{-2}$ is subjected to a load of $250\,N$, then the elongation in the wire will be :

The length of metallic wire is $l$. The tension in the wire is $T_1$ for length $l_1$ and tension in the wire is $T_2$ for length $l_2$. Find the original length.

A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$