An object is taken 1.0 km deep into the sea. Density of sea water = 1.025 × 10³ kg/m³; bulk modulus of the object = 1.6 × 10⁶ kPa. Find the approximate percentage increase in density of the object (take g ≈ 10 m/s²).
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Question

An object is taken 1.0 km deep into the sea. Density of sea water = 1.025 × 10³ kg/m³; bulk modulus of the object = 1.6 × 10⁶ kPa. Find the approximate percentage increase in density of the object (take g ≈ 10 m/s²).

Options

G1 Physics · Accepted Answer

Step 1: Depth h = 1 km = 1000 m; sea-water density ρ = 1.025 × 10³ kg/m³. Step 2: Increase in pressure ΔP = ρgh = 1.025 × 10³ × 10 × 1000 = 1.025 × 10⁷ Pa. Step 3: Convert bulk modulus: B = 1.6 × 10⁶ kPa = 1.6 × 10⁹ Pa. Step 4: For small compression, Δρ/ρ ≈ ΔP/B = 1.025 × 10⁷/(1.6 × 10⁹) = 0.00640625. Step 5: Percentage increase = 0.00640625 × 100 = 0.640625%. Final answer: approximately 0.64% (Option B).