If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10 9 N m - 2 , then fractional compression Δ V V of water at the bottom of ocean is α × 10 - 2 . The value of α is _______, (Given, g = 10 m s - 2 , ρ = 1000 kg m - 3 )

Step-by-step solution

The formula to calculate the Bulk modulus is given by B = - ∆ P ∆ V V . . . 1 From equation (1), the fractional compression in volume may be obtained as follows: - Δ V V = ∆ P B = ρ g ∆ h B . . . 2 From equation (2) it follows that - ∆ V V = 1000 × 10 × 4000 2 × 10 9 ⇒ ∆ V V = 2 × 10 - 2 Hence, α = 2 .