The average depth of Indian ocean is about $3000 \mathrm{~m}$. The value of fractional compression…

The average depth of Indian ocean is about $3000 \mathrm{~m}$. 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 $2.2 \times 10^9 \mathrm{Nm}^{-2}, g=9.8, \rho_{\mathrm{H}_2 \mathrm{O}}=1000 \mathrm{~kg} . \mathrm{m}^{-3}$ )
  1. $3.4 \times 10^{-2}$
  2. $1.34 \times 10^{-2}$
  3. $4.13 \times 10^{-2}$
  4. $13.4 \times 10^{-2}$

Solution

We have, $\begin{aligned} & \frac{\Delta V}{V}=\frac{\mathrm{h} \rho \mathrm{g}}{\mathrm{B}}\left[\because \mathrm{B}=\frac{\Delta \mathrm{P}}{\Delta \mathrm{V} / \mathrm{V}} \Rightarrow \frac{\Delta \mathrm{V}}{\mathrm{V}}=\frac{\Delta \mathrm{P}}{\mathrm{B}}=\frac{\mathrm{h} \rho \mathrm{g}}{\mathrm{B}}\right] \\ & \Rightarrow \quad \frac{\Delta V}{V}=\frac{3 \times 10^3 \times 10^3 \times 9.8}{2.2 \times 10^9}=1.34 \times 10^{-2} \end{aligned}$

Asked in: AP EAMCET 2015

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