Question

The approximate depth of an ocean is 2700 m. The compressibility of water is \( 45.4 \times 10^{-11} \, \text{Pa}^{-1} \) and the density of water is \( 10^3 \, \text{kg m}^{-3} \). What fractional compression of water will be 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 =β ρ g h.

Answer 1

The Correct Option is C

Step 1: Pressure at depth h: P = ρ g h
Step 2: Fractional compression: (Δ V)/(V) = β P = β ρ g h
Step 3: Substituting values: = 45.4×10⁻11 × 10³ × 9.8 × 2700 ≈ 1.2 × 10⁻2 ≈ 1.4 × 10⁻2