State Archimedes Principle. Write its two applications.

A sphere of mass $5 \mathrm{kg}$ and volume $2.2\times {10}^{-4} {\mathrm{m}}^3$ is completely immersed in water. Find the buoyant force exerted by water on the sphere. Density of water$=1000 \mathrm{kg} {\mathrm{m}}^{-3}$. (Given $\mathrm{g}=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

A body is weighed with the help of spring balance and its weight is found to be $30 \mathrm{kgf}$. It is partially immersed in water. Now its weight is found to be $20 \mathrm{kgf}$. Find

(a) the buoyant force.

(b) weight of water displaced.