Q: Estimate the change in the density of water in ocean at a depth of 500 m below the surface. The density of water at the surface = 1030 kgm^{-3} and the bulk modulus of water = 2.2×10^{9} Nm^{-2}

(a) 2.363 kg/m³

(b) 1.363 kg/m³

(c) 4.363 kg/m³

(d) 3.363 kg/m³

Ans: (a)

Sol:

Bulk Modulus of Elasticity is

$ \displaystyle K = \frac{P}{-\Delta V/V} $

$ \displaystyle \frac{-\Delta V}{V} = \frac{P}{K} $

$ \displaystyle \frac{\Delta \rho}{\rho} = \frac{P}{K} $

$ \displaystyle \Delta \rho = \frac{P \rho}{K} $

$ \displaystyle \Delta \rho = \frac{\rho g h \times \rho}{K} $

on putting given values ,

= 2.363 kg/m³