question_answer 42)

                  To what depth must a robber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is\[9.8\times {{10}^{8}}N{{m}^{2}},\] and the density of sea water is\[{{10}^{3}}kg\text{ }{{m}^{3}}\]).                

Answer:

                  \[\frac{\Delta V}{V}=\,0.1%\,=\,\frac{1}{1000}\,=\,{{10}^{-3}}\,\]                             \[P=\,h\,\rho \,g,\] where h is the depth.                 Now \[K=\,\frac{P}{\Delta V/V}\,\,=\,\frac{h\rho g}{\Delta V/V}\]                 or  \[h=\,\frac{\left( \frac{\Delta V}{V} \right)\,k}{\rho g}=\,\frac{{{10}^{-3}}\times 9.8\,\times \,{{10}^{8}}}{{{10}^{3}}\times \,9.8}\]                 \[=100\,m\]