Two wires of same length having radius of $2 \ mm$ and $1.5 \ mm$ respectively are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?

In the determination of Young's modulus $\left(Y=\frac{4 MLg}{\pi \ell d^2}\right)$ by using Searle's method,a wire of length $L=2 \ m$ and diameter $d=0.5 \ mm$ is used. For a load $M=2.5 \ kg$,an extension $\ell=0.25 \ mm$ in the length of the wire is observed. Quantities $d$ and $\ell$ are measured using a screw gauge and a micrometer,respectively. They have the same pitch of $0.5 \ mm$. The number of divisions on their circular scale is $100$. The contributions to the maximum probable error of the $Y$ measurement:

On applying a stress of $20 \times 10^8 \ N/m^2$,the length of a perfectly elastic wire is doubled. Its Young's modulus will be:

$A$ rod of length $L$ at room temperature and uniform area of cross section $A$ is made of a metal having a coefficient of linear expansion $\alpha /^{\circ}C$. It is observed that an external compressive force $F$,applied on each of its ends,prevents any change in the length of the rod when its temperature rises by $\Delta T \, K$. The Young's modulus $Y$ for this metal is:

$A$ wire of length $2 \, m$ is made from copper having a volume of $10 \, cm^3$. When a force $F$ is applied,the extension in its length is $2 \, mm$. If a wire of length $8 \, m$ is made from the same volume of copper,what will be the extension in its length in $cm$ when the same force $F$ is applied?

One end of a steel wire of radius $r$ is fixed to a ceiling and a load of $3 \ kg$ is attached to the free end of the wire. Another wire made of copper of radius $2r$ is attached to the bottom of the $3 \ kg$ load and a $2 \ kg$ load is attached to the free end of the copper wire. The ratio of longitudinal strains produced in copper and steel wires is (Young modulus of steel $= 20 \times 10^{10} \ Nm^{-2}$,Young modulus of copper $= 12 \times 10^{10} \ Nm^{-2}$)