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  4. The average depth of Indian ocean is about 3000 m. The fractional compression, (Δ V/V) of water at the bottom of the ocean is (Given: Bulk modulus of the water = 2.2 × 109 N m-2 and g = 10 m s-2)

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Q. 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 $g = 10 \,m\, s^{-2}$)

Mechanical Properties of Solids

Solution:

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
$\frac{\Delta V}{V}=\frac{P}{B}=\frac{3\times10^{7}\,N\,m^{-2}}{2.2\times10^{9}\,N\,m^{-2}}=1.36\times10^{-2}=1.36\%.$