Question

the average depth of the indian ocean is about 3000m . calculate the fractional compression, deltaV / V, of water at the bottom of the ocean. given that the bulk modulas of water is 2.2 x 10 9 Nm. take g = 10 ms2.

Answer 1

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

Answer 2

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As we know ,

P=−B∆VV

Where B is bulk modulus, and P is the pressure .

Now Pressure at the bottom of the ocean

P=P0+ρgh,

Where P0 is the atmospheric pressure. ρ is density of water and h is the depth of the ocean.

P=P0+ρgh, =105+1000×10×3000=105+3×107=3.01×107 N/m2

Now

∆VV=−PB=3.01×1072.2×109=6.622×10−2

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