The average depth of Red Sea is about 2000 m. Calculate the fractional compression ΔV/V of water at the bottom of the ocean, given that the bulk modulus of water is 2.2 × 109 N m-2. (Take g = 10 m s-2)

Question

Shiksha Nation · Accepted Answer

The pressure exerted by a 2000 m column of water on the bottom layer:

P = ρ g h = 2000 m × 1000 kg m^-3 × 10 m s^-2

= 2 × 10⁷ kg m^-1 s^-2 = 2 × 10⁷ N m^-2

Fractional compression ΔV/V is:

ΔV/V = ^stress/_B = ^{2 × 107 N m-2}/_{2.2 × 10⁹ N m^-2}

= 9.09 × 10^-3 = 0.909%

The average depth of Red Sea is about 2000 m. Calculate the fractional compression ΔV/V of water at the bottom of the ocean, given that the bulk modulus of water is 2.2 × 10⁹ N m^-2. (Take g = 10 m s^-2)

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