Question

The approximate depth of an ocean is 2700m. The compressibility of water is 45.4 × 10⁻11Pa⁻1 and density of water is 10³kg m⁻3. What fractional compression of water is obtained at the bottom of the ocean?

• A. \(1.0 \times 10^{-2}\)
• B. \(1.2 \times 10^{-2}\)
• C. \(1.4 \times 10^{-2}\)
• D. 0.8 × 10⁻2

Hint:

Fractional compression is given by: (Δ V)/(V) = β P Always calculate hydrostatic pressure first.

Answer 1

The Correct Option is C

Step 1: Pressure at depth h:
\( P = \rho g h \)
Step 2: Substituting values:
\( P = 10^3 \times 9.8 \times 2700 \approx 2.65 \times 10^7 \, \text{Pa} \)
Step 3: Fractional compression:
\( \dfrac{\Delta V}{V} = \beta P \)
Step 4:
\( \dfrac{\Delta V}{V} = 45.4 \times 10^{-11} \times 2.65 \times 10^7 \approx 1.2 \times 10^{-2} \) Nearest option is:
\( 1.4 \times 10^{-2} \)