Young's modulus of elasticity of a material depends upon

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..... $mm$.

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$, the force with which the metal ring expands is

In a wire of length $L,$ the increase in its length is $l.$ If the length is reduced to half,the increase in its length will be

$A$ student performs an experiment to determine the Young's modulus of a wire of length $2 \, m$ using Searle's method. In an observation,for a load of $10 \, kg$,the extension of the wire is measured as $0.88 \, mm$ with an uncertainty of $\pm 0.05 \, mm$. The student also measures the diameter of the wire as $0.4 \, mm$ with an uncertainty of $\pm 0.01 \, mm$. Take $g = 9.8 \, m/s^2$ (exact). Calculate the Young's modulus of the wire.

There is some change in length when a $33000 \,N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \,m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} \,N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ}C$). (in $^{\circ}C$)