Due to the addition of impurities,the modulus of elasticity

When a shearing force is applied to a body,elastic potential energy is stored in it. Upon removing the force,this energy:

$A$ substance breaks down by a stress of $10^6 \ N/m^2$. If the density of the material of the wire is $3 \times 10^3 \ kg/m^3$,then the length of the wire of the substance which will break under its own weight when suspended vertically,is ......... $m$.

$A$ uniform wire (Young's modulus $2 \times 10^{11} \, Nm^{-2}$) is subjected to a longitudinal tensile stress of $5 \times 10^7 \, Nm^{-2}$. If the overall volume change in the wire is $0.02\%$,the fractional decrease in the radius of the wire is close to:

The density and breaking stress of a wire are $6 \times 10^4 \ kg/m^3$ and $1.2 \times 10^8 \ N/m^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}$ of the value on the surface of Earth. The maximum length of the wire without breaking is ............ $m$ (take $g = 10 \ m/s^2$ on Earth).

In order to determine the Young's Modulus of a wire of radius $0.2 \, cm$ (measured using a scale of least count $= 0.001 \, cm$) and length $1 \, m$ (measured using a scale of least count $= 1 \, mm$),a weight of mass $1 \, kg$ (measured using a scale of least count $= 1 \, g$) was hanged to get the elongation of $0.5 \, cm$ (measured using a scale of least count $= 0.001 \, cm$). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)