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 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

$A$ constant force is applied to a metal wire of length $L$. The volume of the wire remains constant. The extension produced is proportional to:

$A$ uniform rod of mass $m$,length $L$,area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be

Young's modulus of a material has the same units as

$A$ 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).