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 2.2x 109N/m2.

Answer 1

Answer:

∴ fractional compression = 1.34 × 10⁻²

Explanation:

given,

depth of Indian ocean = 3000 m

Bulk modulus of the water = 2.2 x 10⁹ N/m²

We know,

P = P₀ + ρgh

P₀ is the atmospheric pressure

P₀ = 10⁵ N/m²

ρ is the density of the water, 1000 Kg/m³

P = 10⁵ + 1000 × 9.8 × 3000 = 2.94 × 10⁷ N/m²

using formula,

B = P/{-∆V/V}

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

$\dfrac{-\Delta V}{V} = \dfrac{2.94 \times 10^7}{2.2 \times 10^9}$

$\dfrac{-\Delta V}{V} =1.34 \times 10^{-2}$

∴ fractional compression = 1.34 × 10⁻²