$A$ composite heavy rope made of two materials is suspended vertically from a high ceiling. The ratios of different quantities for the upper rope to the lower rope are: length $\frac{L_u}{L_l} = \frac{1}{2}$,cross-sectional area $\frac{A_u}{A_l} = \frac{2}{1}$,and density $\frac{d_u}{d_l} = \frac{2}{3}$. What is the ratio of the maximum stress in the two ropes?

$A$ tangential force of $100 \,N$ is applied on the top face of a cubic block of side $0.1 \,m$. If the top face is displaced by $0.02 \,cm$ relative to the bottom face,what is the tangential strain?

The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line

The length of a metal wire is $l_{1}$ when the tension in it is $T_{1}$,and it is $l_{2}$ when the tension is $T_{2}$. The natural length of the wire is -

Wires $W_{1}$ and $W_{2}$ are made of the same material having a breaking stress of $1.25 \times 10^{9} \, N/m^{2}$. $W_{1}$ and $W_{2}$ have cross-sectional areas of $8 \times 10^{-7} \, m^{2}$ and $4 \times 10^{-7} \, m^{2}$,respectively. Masses of $20 \, kg$ and $10 \, kg$ hang from them as shown in the figure. The maximum mass $m$ that can be placed in the pan without breaking the wires is $..... \, kg$. (Use $g = 10 \, m/s^{2}$)

State Hooke's law.