Question
State Hook's law. Calculate the fractional AV compression, $\frac{\Delta\text{V}}{\text{V}},$ of water at the bottom of the ocean having depth 3000m. The bulk modulus of water is $2.2 \times 10^9Nm^{-2}$. (Take g $= 10ms^{-2})$
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Answer
Hook's law: Within the elastic limits the ratio between stress and strain is constant and is called modulus of elasticity. $\frac{\text{Stress}}{\text{Strain}}=\text{Modulus of elasticity}$ Given depth h $=3000\text{m},\rho=10^3\text{kg/m}^3,\text{g}=10\text{ms}^{-2}$ $\text{p}=\text{h}\rho\text{g}=3000\times10^3\times10$ $=3\times10^7\text{Nm}^{-2}$ Bulk modulus $=\frac{\Delta\text{P}}{\Delta\frac{\text{V}}{\text{V}}},$ $\frac{\Delta\text{V}}{\text{V}}=\frac{\Delta\text{P}}{\text{B}}=\frac{3\times10^7}{2.2\times10^9}=1.36\times10^{-2}$
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