Two wires $A$ and $B$ are made of the same material having a ratio of lengths $\frac{L_A}{L_B} = \frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B} = 2$. If both the wires are stretched using the same force,what would be the ratio of their respective elongations?

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 $= 12 \times 10^{10} \ Nm^{-2}$)

The length of an iron wire is $L$ and the area of cross-section is $A$. The increase in length is $l$ upon applying a force $F$ on its two ends. Which of the following statements is correct?

The Young's modulus of a wire is $Y$. If the energy per unit volume is $E$,then the strain will be

Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths,radii,and Young's modulus of wires $A$ and $B$ are $r, 2r$,and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if the ratio of the increase in their corresponding lengths is $1/(6r^2)$. The mass of block $Q$ is $3M$.

The lengths of four wires $A, B, C$ and $D$ made of the same material are $1 \,m, 2 \,m, 3 \,m$ and $4 \,m$ respectively. The radii of the wires $A, B, C$ and $D$ are $0.2 \,mm, 0.4 \,mm, 0.6 \,mm$ and $0.8 \,mm$ respectively. For the same applied tension, the elongation is more in which wire?