The area of cross-section of a steel wire $(Y = 2.0 \times 10^{11} \ N/m^2)$ is $0.1 \ cm^2$. The force required to double its length will be

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:

An area of cross-section of a rubber string is $2 \, cm^2$. Its length is doubled when stretched with a linear force of $2 \times 10^5 \, dynes$. The Young's modulus of the rubber in $dyne/cm^2$ will be:

$A$ wire extends by $1 \ mm$ when a force is applied. If double the force is applied to another wire of the same material and length but half the radius of the cross-section,what will be the elongation of the wire in $mm$?

$A$ steel wire $1.5\,m$ long and of radius $1\,mm$ is attached with a load of $3\,kg$ at one end,while the other end is fixed. It is whirled in a vertical circle with a frequency of $2\,Hz$. Find the elongation of the wire when the weight is at the lowest position. (Given: $Y = 2 \times 10^{11}\,N/m^2$ and $g = 10\,m/s^2$)

$A$ rod $BC$ of negligible mass is 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 the figure. For the rod $BC$,length $L = 4 \ m$,area of cross-section $A = 4 \times 10^{-4} \ m^2$,Young's modulus $Y = 10^{11} \ N/m^2$ and coefficient of linear expansion $\alpha = 2.2 \times 10^{-4} \ K^{-1}$. If the rod $BC$ is cooled from temperature $100^oC$ to $0^oC$,then find the decrease in length of the rod in centimeters (closest to the integer).