$A$ body of mass $10 \, kg$ is attached to the end of a wire of length $0.3 \, m$. If the breaking stress of the wire is $4.8 \times 10^7 \, N/m^2$ and its cross-sectional area is $10^{-6} \, m^2$,what is the maximum angular velocity in $rad/sec$ with which it can be rotated in a horizontal plane without breaking the wire?

Write the formula,dimensional formula,and $SI$ unit for the Shear Modulus and the Bulk Modulus.

Two blocks of masses $1 \, kg$ and $2 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 \, N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 \, m/s^2$.

The two thigh bones (femurs),each of cross-sectional area $10 \; cm^{2}$,support the upper part of a human body of mass $40 \; kg$. Estimate the average pressure sustained by the femurs.

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.

The density and breaking stress of a wire are $6 \times 10^4 \ kg/m^3$ and $1.2 \times 10^8 \ N/m^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}$ of the value on the surface of Earth. The maximum length of the wire without breaking is ............ $m$ (take $g = 10 \ m/s^2$ on Earth).