Question

the average depth of Indian Ocean is about 3000m. calculate the fractional compression,∆v/v, of water at the bottom of the ocean,given that the bulk modulus of water is 2.2*10⁹N/m².​

Answer 1

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Class 11

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>>Mechanical Properties of Solids

>>Shear Modulus and Bulk Modulus

>>The average depth of Indian Ocean is abo

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The average depth of Indian Ocean is about 3000 m. Calculate the fractional compression,

V

ΔV

of water at the bottom of the ocean, given that the bulk modulus of water is 2.2×10

9

Nm

−2

(consider g=10ms

−2

)

Medium

Solution

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Correct option is D)

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

so the answer is 1.36 percent

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