Stress required in a wire to produce $0.1\%$ strain is $4 \times 10^8 \, N/m^2$. Its Young's modulus is $Y_1$. If stress required in another wire to produce $0.3\%$ strain is $6 \times 10^8 \, N/m^2$,and its Young's modulus is $Y_2$,which relation is correct?

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.

Two wires of the same length and radius are joined end-to-end and loaded. The Young's moduli of the materials of the two wires are $Y_{1}$ and $Y_{2}$. If the combination behaves as a single wire,then its equivalent Young's modulus is:

The diameter of a brass rod is $4 \ mm$ and Young's modulus of brass is $9 \times 10^{10} \ N/m^2$. The force required to stretch it by $0.1\%$ of its original length is:

$A$ wire of area of cross-section $10^{-6} \ m^2$ is increased in length by $0.1 \%$. The tension produced is $1000 \ N$. The Young's modulus of the wire is:

One end of a steel rod of radius $10.0 \ mm$ and length $50.0 \ cm$ is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude $10.0 \times \pi \ kN$. This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus $= 2.0 \times 10^{11} \ N/m^2$) (in $mm$)