Question

The average depth of Indian ocean is about $3000\, m$. The fractional compression, $\frac{\Delta V}{V}$ of water at the bottom of the ocean is (Given : Bulk modulus of the water $= 2.2 ? 10^9 \,N \,m^{-2}$ and $g = 10 \,m\, s^{-2}$)

• A. 0.82%
• B. 0.91%
• C. 1.36%
• D. 1.24%

Answer 1

Answer: (C)

1.36%

Answer 2

The pressure exerted by a 3000 m column of water on the bottom layer is $P=h\rho g$ $= 3000 \,m ? 1000 \,kg \,m^{-3} ? 10\, m\, s^{-2}$ $=3\times10^{7}\,N\,m^{-2}$ Fractional compression $\frac{\Delta V}{V}$ is $\frac{\Delta V}{V}=\frac{P}{B}=\frac{3\times10^{7}\,N\,m^{-2}}{2.2\times10^{9}\,N\,m^{-2}}=1.36\times10^{-2}=1.36\%.$