The average depth of Indian ocean is about $3000 m$ . The value of fractional compression $(\frac{Δ V}{V})$ of water at the bottom of the ocean is (given that the bulk modulus of water is $2.2 \times 10^{9} N m^{- 2}, g = 9.8 m s^{- 2}, ρ_{H_{2} O} = 1000 k g . m^{- 3}$ )

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$1.34 \times 10^{- 2}$

$4.13 \times 10^{- 2}$

$3.4 \times 10^{- 2}$

$13.4 \times 10^{- 2}$

answer is B.

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Detailed Solution

The fractional compression or decrease in volume $\frac{Δ V}{V} = \frac{h ρ g}{k} (∵ B = \frac{- Δ P}{\frac{Δ V}{V}})$

$\Rightarrow \frac{Δ V}{V} = \frac{3 \times 10^{3} \times 10^{3} \times 9.8}{2.2 \times 10^{9}} = \frac{3}{2.2} \times 10^{- 4} \times 98$

$= \frac{147}{1.1} \times 10^{- 4} = 1.34 \times 10^{- 2}$

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