Question

The average depth of Indian Ocean is about 3000 m. Calculate the fractional compression,$\frac{\Delta V}{V}$ of water at the bottom of the ocean, given that the bulk modulus of water is $2.2\times {10}^{9}N{m}^{-2}$ (consider $g=10m{s}^{-2}$)

• A. 0.82%
• B. 0.91%
• C. 1.24%
• D. 1.36%

Answer 1

The correct option is D 1.36%

We know one thing

P = P₀ + ρgh

Where P₀ is the atmospheric pressure , g is acceleration due to gravity, h is the height from the Earth surface and ρ is density of water

Here, P₀ = 10⁵ N/m² , g = 10m/s² , h = 3000m and ρ = 10³ Kg/m³

Now, P = 10⁵ + 10³ × 10 × 3000 = 3.01 × 10⁷ N/m²

Again, we have to use formula,

B = P/{-∆V/V}

Here, B is bulk modulus and { -∆V/V} is the fractional compression

So, -∆V/V = P/B

Put , P = 3.01 × 10⁷ N/m² and B= 2.2 × 10⁹ N/m²

∴ fractional compression = 3.01 × 10⁷/2.2 × 10⁹ = 1.368 × 10⁻²

Hence the ans is D