$A$ rod of constant cross-section moves towards the right with constant acceleration $a$. The graph of stress versus distance from the left end is shown in the figure. If the density of the material of the rod at cross-section $1$ is $9 \text{ g/cm}^3$,find the density at cross-section $2$ in $\text{g/cm}^3$.

$A$ lift is tied with thick iron ropes having mass $M$. The maximum acceleration of the lift is $a \ m/s^2$ and the maximum safe stress is $s \ N/m^2$. The minimum diameter of the rope is $(g = \text{acceleration due to gravity})$

One end of a uniform rod of mass $m_1$ and cross-sectional area $A$ is hung from a ceiling. The other end of the rod is supporting a mass $m_2$. The stress at the midpoint of the rod is:

$A$ 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?

What is a yield point? What is a yield strength?

$A$ bar of cross-sectional area $A$ is subjected to two equal and opposite tensile forces at its ends as shown in the figure. Consider a plane $BB'$ making an angle $\theta$ with the length. The ratio of tensile stress to the shearing stress on the plane $BB'$ is