$A$ uniform metallic wire is elongated by $0.04\, m$ when subjected to a linear force $F$. The elongation,if its length and diameter are doubled and subjected to the same force,will be ..... $cm$.

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

The ratio of the lengths of two wires $A$ and $B$ of the same material is $1 : 2$ and the ratio of their diameters is $2 : 1$. If they are stretched by the same force,what is the ratio of the increase in their lengths?

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 $\,mm$)

Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is $0.5 \ cm$,find the elongation $(l)$ of each wire. Given: ${Y_s} = 2.0 \times {10^{11}} \ N/m^2$ and ${Y_c} = 1.2 \times {10^{11}} \ N/m^2$.

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$