What is the tangential stress on the cross-section $PQRS$?

$A$ solid that transmits light in the visible region and has a very low melting point possesses:

$A$ wire of density $3 \times 10^3 \, kg/m^3$ requires a breaking stress of $10^6 \, N/m^2$ to break. What should be the length of the wire so that it breaks under its own weight? (Take $g = 10 \, m/s^2$)

If the breaking stress of a wire is $3.18 \times 10^{10} \, N/m^2$,what should be its minimum radius so that the wire does not break? (Refer to the figure for the masses attached to the pulley system,assume $g = 10 \, m/s^2$)

$A$ string of length $0.314 \text{ m}$ and Young's modulus $2 \times 10^{10} \text{ N/m}^2$ is connected to another string of length $B$ and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass $0.8 \text{ kg}$. The net change in length of the combination is . . . . . . $\text{mm}$. (radius of both the strings is $0.2 \text{ mm}$ and acceleration due to gravity $= 10 \text{ m/s}^2$) (Mass of both strings is to be neglected as compared to the mass of load)

Two strips of metal are riveted together at their ends by four rivets,each of diameter $6.0\; mm$. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed $6.9 \times 10^{7}\; Pa$? Assume that each rivet is to carry one quarter of the load.