Find the elastic potential energy per unit volume of water (in $\times {10}^3{\mathrm{Jm}}^{-3}$) at a depth of $1 \mathrm{km}.$ Given, compressibility of water $=5\times {10}^{10}\mathrm{SI}$ units and density of water $=1000 \mathrm{kg}{ \mathrm{m}}^{-3}.$

A ring of radius $r$ (made of wire of density $\rho$ ) placed on a smooth horizontal surface is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in figure. Determine the angular velocity in $\mathrm{rad}/\mathrm{s}$ at which the ring breaks. The wire breaks at a tensile stress \sigma. (given $\sigma /\rho =9 \mathrm{N}-\mathrm{m}/\mathrm{kg}$ and $r=1 \mathrm{m}$)