In the $CGS$ system,the Young's modulus of a steel wire is $2 \times 10^{12} \text{ dyn/cm}^2$. To double the length of a wire of unit cross-sectional area,the force required is:

$A$ steel wire of length $L$ and area of cross-section $A$ is suspended from a rigid support. If $Y$ is the Young's modulus of the material of the wire and $\alpha$ is the coefficient of linear expansion,then the increase in tension when the temperature falls by $t^{\circ} C$ is:

An object of mass $15 \,kg$ is attached to the end of a metal wire of unstretched length $1.0 \,m$. The object is then whirled in a vertical circle with an angular velocity of $4 \,rad/s$ at the bottom of the circle. If the cross-sectional area of the wire is $0.05 \,cm^2$ and Young's modulus of the metal is $2 \times 10^{11} \,N/m^2$, then calculate the elongation of the wire when the mass is at the lowest point of its path. (Take $g = 10 \,m/s^2$) (in $\,mm$)

The following four wires are made of the same material. Which one will have the largest elongation when subjected to the same tension?

$A$ horizontal steel railroad track has a length of $100 \, m$ when the temperature is $25^{\circ} C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day,when the temperature is $40^{\circ} C$,is ............. $\times 10^7 \, Pa$. (Note: The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5} /^{\circ} C$ and the Young's modulus of steel is $2 \times 10^{11} \, Pa$.)

At $40\,^oC$,a brass wire of radius $0.5\, mm$ (diameter $1\, mm$) is hung from the ceiling. $A$ small mass $M$ is hung from the free end of the wire. When the wire is cooled down from $40\,^oC$ to $20\,^oC$,it regains its original length of $0.2\, m$. The value of $M$ is close to ........$kg$. (Coefficient of linear expansion $\alpha = 10^{-5}/^oC$ and Young's modulus $Y = 10^{11}\, N/m^2$; $g = 10\, ms^{-2}$)