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..... $mm$

A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is

A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$

A $100\,m$ long wire having cross-sectional area $6.25 \times 10^{-4}\,m ^2$ and Young's modulus is $10^{10}\,Nm ^{-2}$ is subjected to a load of $250\,N$, then the elongation in the wire will be :

Young's modulus depends upon

The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress ?