A horizontally oriented copper rod of length $l=1 \mathrm{m}$ is rotated about a vertical axis passing through its middle. What is the number of $r.p.s.$ at which this rod ruptures? Breaking or rupture strength of copper is $\sigma$ and density of copper is $\rho$.

What work has to be performed to make a hoop out of a steel band of length $l$, width $h$ and thickness $\delta$? The process is assumed to proceed within the elasticity range of the material.

A catapult is stretched with a force of $100 \mathrm{N}$ which changes the length of the band from $10 \mathrm{cm}$ to $14 \mathrm{cm}$. Find the velocity with which a stone of mass $1 \mathrm{kg}$ will leave the catapult when aimed at a mango.