Question

The average depth of Indian ocean is about $ 3000\, m $ . The value of fractional compression $ \left(\frac{\Delta V}{V}\right) $ of water at the bottom of the ocean is (given that the bulk modulus of water is $ 2.2 \times10^{9}\,Nm^{-2} $ , $ g=9.8 $ , $ \rho_{H_2O}=1000\,kg.m^{-3} $ )

• A. $ 3.4 \times 10^{-2} $
• B. $ 1.34 \times 10^{-2} $
• C. $ 4.13 \times 10^{-2} $
• D. $ 13.4 \times 10^{-2} $

Answer 1

Answer: (B)

The fractional compression or decrease in volume
$\frac{\Delta V}{V}=\frac{h \rho g}{k}$
where, $h=$ depth (average)
$\rho=$ density of ocean water
$g=$ gravitational acceleration and
$k=$ bulk modulus
$ \Rightarrow \frac{\Delta V}{V} =\frac{3 \times 10^{3} \times 10^{3} \times 9.8}{2.2 \times 10^{9}} $
$ =\frac{3}{2.2} \times 10^{-4} \times 98 $
$=\frac{147}{11} \times 10^{-4}=1.34 \times 10^{-2} $