Solids: Practice Problem & Solution
The approximate depth of an ocean is $2700 \text{ m}$. The compressibility of water is $45.4 \times 10^{-11} \text{ Pa}^{-1}$ and density of water is $10^3 \text{ kg/m}^3$. What fractional compression of water will be obtained at the bottom of the ocean? (2015)
Solution Explained:
To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:
Pressure at depth $h$ is $$P = \rho gh = 10^3 \times 9.8 \times 2700 \approx 26.4 \times 10^6 \text{ Pa}$$. Fractional compression is $$\frac{\Delta V}{V} = P \times K = (26.4 \times 10^6) \times (45.4 \times 10^{-11}) \approx 1.2 \times 10^{-2}$$.
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