The shear modulus of lead is $2\times {10}^9 \mathrm{Pa}$. A cubic lead slab of side $50 \mathrm{cm}$ is subjected to a shearing force of magnitude $9\times {10}^4 \mathrm{N}$ on its narrow face. The displacement of upper edge is $\Delta l$

What internal pressure in the absence of external pressure can be sustained by a glass spherical flask if in both the cases, wall thickness is equal to $\Delta r=1\mathrm{mm}$ and radius of tube and the flask equals $r=25$ $\mathrm{mm}$? $(\mathrm{S}=493\mathrm{SI}$ $\mathrm{units}$$)$

A steel cylindrical rod of length $l$ and radius $r$ is suspended by its end from the ceiling. Find the elastic deformation energy $U$of the rod.

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.