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 = 2.2×109 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