Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

The cross-sectional area of each wire is $10^{-4} \, m^2$. What is the displacement of point $B$?

$A$ thick brass wire of length $L$ and density $\rho$ is suspended from a rigid support. Due to its own weight,$\ell$ is the increase in length. The Young's modulus $Y$ of the brass wire in terms of density is $(g = \text{acceleration due to gravity})$

When a weight of $10 \,kg$ is suspended from a copper wire of length $3 \,m$ and diameter $0.4 \,mm$, its length increases by $2.4 \,cm$. If the diameter of the wire is doubled, then the extension in its length will be (in $\,cm$)

$A$ force of $200\, N$ is applied at one end of a wire of length $2\, m$ and having area of cross-section $10^{-2}\, cm^2$. The other end of the wire is rigidly fixed. If the coefficient of linear expansion of the wire is $\alpha = 8 \times 10^{-6}\, ^\circ C^{-1}$,Young's modulus is $Y = 2.2 \times 10^{11}\, N/m^2$,and its temperature is increased by $5\, ^\circ C$,then the increase in the tension of the wire will be ........ $N$.

The cross-sectional area of all wires is $10^{-4} \ m^2$. What is the displacement of point $D$?