$A$ 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

The Young's modulus of a wire of length $L$ and radius $r$ is $Y \, N/m^2$. What will be the Young's modulus of a wire made of the same material with length $L/2$ and radius $r/2$?

Overall changes in volume and radii of a uniform cylindrical steel wire are $0.2 \%$ and $0.002 \%$ respectively when subjected to some suitable force. Calculate the longitudinal tensile stress acting on the wire. (Given: Young's modulus $Y = 2.0 \times 10^{11} \ N/m^2$)

Which is more elastic: rubber or steel?

$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

The extension of a wire by the application of load is $3 \ mm$. The extension in a wire of the same material and length but half the radius by the same load is..... $mm$.